
  
                                     
                      DRC: Digital Room Correction
                      ****************************
                             Denis Sbragion
                             ==============
                               2010-01-01 
                              ============
                                    
                Copyright (c) 2002-2010 Denis Sbragion 
                =======================================
                                    
                             Version 3.1.0 
                             ==============
  
  
   
  This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2 of the License, or (at your
option) any later version. 
  
  This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General
Public License for more details. 
  
  You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 675 Mass Ave, Cambridge, MA 02139, USA. 
  
  You can contact the author on Internet at the following address:
    d.sbragion@infotecna.it 
  
  This program uses the parsecfg library from Yuuki NINOMIYA. Details on
this library can be found in the parsecfg.c and parsecfg.h files. Many
thanks to Yuuki NINOMIYA for this useful library. 
  
  This program uses also the FFT routines from Takuya Ooura and the GNU
Scientific Library (GSL) FFT routines. Many thanks to Takuya Ooura and
the GSL developers for these efficient routines.
  

Contents
*=*=*=*=

   
  
   - 1  Introduction 
   - 2  Getting the latest version 
   - 3  What's new in version 3.1.0 
     
      - 3.1  Compatibility with previous versions 
      - 3.2  History: what was new in previous versions 
        
         - 3.2.1  Version 3.0.1 
         - 3.2.2  Version 3.0.0 
         - 3.2.3  Version 2.7.0 
         - 3.2.4  Version 2.6.2 
         - 3.2.5  Version 2.6.1 
         - 3.2.6  Version 2.6.0 
         - 3.2.7  Version 2.5.1 
         - 3.2.8  Version 2.5.0 
         - 3.2.9  Version 2.4.2 
         - 3.2.10  Version 2.4.1 
         - 3.2.11  Version 2.4.0 
         - 3.2.12  Version 2.3.2 
         - 3.2.13  Version 2.3.1 
         - 3.2.14  Version 2.3.0 
         - 3.2.15  Version 2.2.0 
         - 3.2.16  Version 2.1.0 
         - 3.2.17  Version 2.0.0 
         - 3.2.18  Version 1.3.0 
     
  
   - 4  Program description and operation 
     
      - 4.1  Filter generation procedure 
      - 4.2  Frequency dependent windowing 
        
         - 4.2.1  Pre-echo truncation 
         - 4.2.2  Ringing truncation stage 
     
      - 4.3  Psychoacoustic target computation 
      - 4.4  Impulse response measurement 
        
         - 4.4.1  The glsweep program 
         - 4.4.2  The lsconv program 
         - 4.4.3  Sample automated script file 
         - 4.4.4  Beware cheap, resampling, soundcards 
         - 4.4.5  How to work around your cheap, resampling, soundcard 
     
      - 4.5  Sample rate conversion 
      - 4.6  Correction tuning 
        
         - 4.6.1  Preventing pre-echo artifacts 
         - 4.6.2  Preventing clipping 
         - 4.6.3  Some notes about loudspeaker placement 
         - 4.6.4  Some notes about channel balance 
         - 4.6.5  Interchannel time alignment 
         - 4.6.6  How to tune the filters for your audio system 
     
  
   - 5  Program compilation and execution 
     
      - 5.1  Command line parameters replacing 
      - 5.2  Sample configuration files 
        
         - 5.2.1  Target magnitude response 
     
  
   - 6  DRC Configuration file reference 
     
      - 6.1  BC - Base Configuration 
        
         - 6.1.1  BCBaseDir 
         - 6.1.2  BCInFile 
         - 6.1.3  BCInFileType 
         - 6.1.4  BCSampleRate 
         - 6.1.5  BCImpulseCenterMode 
         - 6.1.6  BCImpulseCenter (*) 
         - 6.1.7  BCInitWindow 
         - 6.1.8  BCPreWindowLen 
         - 6.1.9  BCPreWindowGap 
         - 6.1.10  BCNormFactor 
         - 6.1.11  BCNormType 
         - 6.1.12  BCDLType, BCDLMinGain, BCDLStartFreq, BCDLEndFreq,
         BCDLStart,  BCDLMultExponent 
     
      - 6.2  MC - Microphone Compensation 
        
         - 6.2.1  MCFilterType 
         - 6.2.2  MCInterpolationType 
         - 6.2.3  MCMultExponent 
         - 6.2.4  MCFilterLen 
         - 6.2.5  MCNumPoints 
         - 6.2.6  MCPointsFile 
         - 6.2.7  MCMagType 
         - 6.2.8  MCFilterFile 
         - 6.2.9  MCOutWindow 
         - 6.2.10  MCNormFactor 
         - 6.2.11  MCNormType 
         - 6.2.12  MCOutFile 
         - 6.2.13  MCOutFileType 
     
      - 6.3  HD - Homomorphic Deconvolution 
        
         - 6.3.1  HDMultExponent 
         - 6.3.2  HDMPNormFactor 
         - 6.3.3  HDMPNormType 
         - 6.3.4  HDMPOutFile 
         - 6.3.5  HDMPOutFileType 
         - 6.3.6  HDEPNormFactor 
         - 6.3.7  HDEPNormType 
         - 6.3.8  HDEPOutFile 
         - 6.3.9  HDEPOutFileType 
     
      - 6.4  MP - Minimum phase Prefiltering 
        
         - 6.4.1  MPPrefilterType 
         - 6.4.2  MPPrefilterFctn 
         - 6.4.3  MPWindowGap 
         - 6.4.4  MPLowerWindow (*) 
         - 6.4.5  MPUpperWindow (*) 
         - 6.4.6  MPStartFreq 
         - 6.4.7  MPEndFreq 
         - 6.4.8  MPWindowExponent (*) 
         - 6.4.9  MPFilterLen 
         - 6.4.10  MPFSharpness (*) 
         - 6.4.11  MPBandSplit 
         - 6.4.12  MPHDRecover 
         - 6.4.13  MPEPPreserve 
         - 6.4.14  MPHDMultExponent 
         - 6.4.15  MPPFFinalWindow 
         - 6.4.16  MPPFNormFactor 
         - 6.4.17  MPPFNormType 
         - 6.4.18  MPPFOutFile 
         - 6.4.19  MPPFOutFileType 
     
      - 6.5  DL - Dip Limiting 
        
         - 6.5.1  DLType 
         - 6.5.2  DLMinGain 
         - 6.5.3  DLStartFreq 
         - 6.5.4  DLEndFreq 
         - 6.5.5  DLStart 
         - 6.5.6  DLMultExponent 
     
      - 6.6  EP - Excess phase Prefiltering 
        
         - 6.6.1  EPPrefilterType 
         - 6.6.2  EPPrefilterFctn 
         - 6.6.3  EPWindowGap 
         - 6.6.4  EPLowerWindow (*) 
         - 6.6.5  EPUpperWindow (*) 
         - 6.6.6  EPStartFreq 
         - 6.6.7  EPEndFreq 
         - 6.6.8  EPWindowExponent (*) 
         - 6.6.9  EPFilterLen 
         - 6.6.10  EPFSharpness (*) 
         - 6.6.11  EPBandSplit 
         - 6.6.12  EPPFFinalWindow 
         - 6.6.13  EPPFFlatGain 
         - 6.6.14  EPPFOGainFactor 
         - 6.6.15  EPPFFlatType 
         - 6.6.16  EPPFFGMultExponent 
         - 6.6.17  EPPFNormFactor 
         - 6.6.18  EPPFNormType 
         - 6.6.19  EPPFOutFile 
         - 6.6.20  EPPFOutFileType 
     
      - 6.7  PC - Prefilter Completion 
        
         - 6.7.1  PCOutWindow 
         - 6.7.2  PCNormFactor 
         - 6.7.3  PCNormType 
         - 6.7.4  PCOutFile 
         - 6.7.5  PCOutFileType 
     
      - 6.8  IS - Inversion Stage 
        
         - 6.8.1  ISType 
         - 6.8.2  ISPETType 
         - 6.8.3  ISPrefilterFctn 
         - 6.8.4  ISPELowerWindow 
         - 6.8.5  ISPEUpperWindow 
         - 6.8.6  ISPEStartFreq 
         - 6.8.7  ISPEEndFreq 
         - 6.8.8  ISPEFilterLen 
         - 6.8.9  ISPEFSharpness 
         - 6.8.10  ISPEBandSplit 
         - 6.8.11  ISPEWindowExponent 
         - 6.8.12  ISPEOGainFactor 
         - 6.8.13  ISSMPMultExponent 
         - 6.8.14  ISOutWindow 
         - 6.8.15  ISNormFactor 
         - 6.8.16  ISNormType 
         - 6.8.17  ISOutFile 
         - 6.8.18  ISOutFileType 
     
      - 6.9  PT - Psychoacoustic Target 
        
         - 6.9.1  PTType 
         - 6.9.2  PTReferenceWindow (*) 
         - 6.9.3  PTDLType, PTDLMinGain, PTDLStartFreq, PTDLEndFreq,
         PTDLStart,  PTDLMultExponent 
         - 6.9.4  PTBandWidth (*) 
         - 6.9.5  PTPeakDetectionStrength (*) 
         - 6.9.6  PTMultExponent 
         - 6.9.7  PTFilterLen 
         - 6.9.8  PTFilterFile 
         - 6.9.9  PTFilterFileType 
         - 6.9.10  PTNormFactor 
         - 6.9.11  PTNormType 
         - 6.9.12  PTOutFile 
         - 6.9.13  PTOutFileType 
         - 6.9.14  PTOutWindow 
     
      - 6.10  PL - Peak Limiting 
        
         - 6.10.1  PLType 
         - 6.10.2  PLMaxGain 
         - 6.10.3  PLStart 
         - 6.10.4  PLStartFreq 
         - 6.10.5  PLEndFreq 
         - 6.10.6  PLMultExponent 
         - 6.10.7  PLOutWindow 
         - 6.10.8  PLNormFactor 
         - 6.10.9  PLNormType 
         - 6.10.10  PLOutFile 
         - 6.10.11  PLOutFileType 
     
      - 6.11  RT - Ringing Truncation 
        
         - 6.11.1  RTType 
         - 6.11.2  RTPrefilterFctn 
         - 6.11.3  RTWindowGap 
         - 6.11.4  RTLowerWindow (*) 
         - 6.11.5  RTUpperWindow (*) 
         - 6.11.6  RTStartFreq 
         - 6.11.7  RTEndFreq 
         - 6.11.8  RTWindowExponent (*) 
         - 6.11.9  RTFilterLen 
         - 6.11.10  RTFSharpness (*) 
         - 6.11.11  RTBandSplit 
         - 6.11.12  RTOutWindow 
         - 6.11.13  RTNormFactor 
         - 6.11.14  RTNormType 
         - 6.11.15  RTOutFile 
         - 6.11.16  RTOutFileType 
     
      - 6.12  PS - Postfiltering Stage 
        
         - 6.12.1  PSFilterType 
         - 6.12.2  PSInterpolationType 
         - 6.12.3  PSMultExponent 
         - 6.12.4  PSFilterLen 
         - 6.12.5  PSNumPoints 
         - 6.12.6  PSMagType 
         - 6.12.7  PSPointsFile (*) 
         - 6.12.8  PSOutWindow 
         - 6.12.9  PSNormFactor 
         - 6.12.10  PSNormType 
         - 6.12.11  PSOutFile 
         - 6.12.12  PSOutFileType 
     
      - 6.13  MS - Minimum phase filter extraction Stage 
        
         - 6.13.1  MSMultExponent 
         - 6.13.2  MSOutWindow 
         - 6.13.3  MSFilterDelay 
         - 6.13.4  MSNormFactor 
         - 6.13.5  MSNormType 
         - 6.13.6  MSOutFile 
         - 6.13.7  MSOutFileType 
     
      - 6.14  TC - Test Convolution 
        
         - 6.14.1  TCNormFactor 
         - 6.14.2  TCNormType 
         - 6.14.3  TCOutFile 
         - 6.14.4  TCOutFileType 
     
  
   - 7  Acknowledgments 
   - 8  Similar software 
   - 9  Commercial products 
   - A  Sample results 
     
      - A.1  Time response 
      - A.2  Frequency response 
      - A.3  Phase response 
      - A.4  Time-frequency analysis 
      - A.5  Wavelet cycle-octave analysis 
      - A.6  Baseline 
        
         - A.6.1  Baseline time response 
         - A.6.2  Baseline frequency response 
         - A.6.3  Baseline phase response 
         - A.6.4  Baseline time-frequency analysis 
         - A.6.5  Baseline wavelet cycle-octave analysis 
     
  
   
  

1  Introduction
*=*=*=*=*=*=*=*

  
  DRC uses a lot of signal, linear system and DSP theory to achieve its
results. In this user manual some knowledge about those arguments is
assumed. I'm planning to write a more extensive manual with the basics
needed to understand what DRC does, or at least is trying to do, but
unfortunately I have just little spare time to dedicate to this project,
so I will concentrate just on improving the program performances. Of
course volunteers, suggestion, patches, better documentation, pointers
and references on the subject are all appreciated.
  For a basic introductory guide to DSP theory and practice you might
look at:
    http://www.dspguide.com/ 
   For a basic introduction to DSP applied to audio you might read the
good book available at:
    http://profs.sci.univr.it/~rocchess/htmls/corsi/SoundProcessing/Soun
   dProcessingBook/ 
   To better understand what DRC is trying to do you might look at:
    http://en.wikipedia.org/wiki/Digital_Room_Correction 
   This clear and concise Wikipedia article contains all the basics
needed to understand digital room correction in general. Another
interesting page is available at:
    http://www.ludd.luth.se/~torger/filter.html 
   On this web page you'll find some good explanations about the Nwfiir
Audio Tools suite, which was a project, now discontinued, similar to DRC
but implemented using warped FIR filters instead of the usual standard
FIR filters.
  Compared with the Nwfiir Audio Tools suite DRC does only the job
carried out by the wfird program, generating just the FIR filters for
digital room correction. 
  In order to measure the room impulse response and to perform real time
or offline convolution (i.e. the correction) of the digital signal, you
have to use some external programs, like, for example, BruteFIR (see
section 2).
  A good DRC step by step guide has been written by "Jones Rush", and it
is available at the following URL:
  
    http://www.duffroomcorrection.com/images/d/de/DRC_Guide_v1.0.pdf 
   "Jones Rush" spent quite a lot of time learning the complete
procedure needed to set up a full digital room correction system and
also spent a lot of time writing the guide from the beginner's point of
view, so this is a really good starting point for everyone who has never
played before with this sort of things. The guide is now a bit outdated,
but despite this it is still a valid reference for the whole procedure
of  DRC filters creation. The main difference is in the name of the
output file generated by the latest sample configuration files, which
now is "rps.pcm" instead of "dxf.pcm".
  Ed Wildgoose is trying to create a collaborative documentation effort
at:
    http://www.duffroomcorrection.com/ 
   Please, take the time to improve the available documentation and to
share your experience participating to those nice Wiki pages. It could
be really useful for other DRC users.
  

2  Getting the latest version
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*

  
  The official DRC web site is available at the following address: 	 
    http://drc-fir.sourceforge.net/ 
   On the web site you will always find news and up to date
informations, the full documentation for the latest version,
informations about where to download it and many other DRC related
informations. New DRC releases are announced using the Freshmeat
announcement and tracking service. The Freshmeat DRC page is available
at the following address: 	 
    http://freshmeat.net/projects/drc/ 
  
  

3  What's new in version 3.1.0
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=

  
  The Octave scripts have been reworked to make them compatible with the
 latest version of Octave and improved to provide some autoscaling 
features and exports to different image formats. The microphone 
compensation stage has been moved to the beginning of the correction 
procedure so that any following stage works using the compensated 
impulse response as a reference. A new parameter adding a configurable 
delay to the minimum phase version of the correction filter has been 
introduced. Many other minor bugs have been fixed. 
  

3.1  Compatibility with previous versions
=========================================
  
  Configuration files for version 3.0.1 are not compatible with the
current  version but could be easily adapted to the current version.
  

3.2  History: what was new in previous versions
===============================================
  
  

3.2.1  Version 3.0.1
--------------------
  
  The Octave scripts have been reworked to make them compatible with 
version 3 of Octave. A new renormalization procedure, providing a 
reasonable extimation of clipping levels, has been added. Many minor 
bugs have been fixed. 
  

3.2.2  Version 3.0.0
--------------------
  
  A new method for the computation of an optimized psychoacoustic target
 response, based on the spectral envelope of the corrected impulse 
response, has been introduced. 
  

3.2.3  Version 2.7.0
--------------------
  
  A new method for the computation of the excess phase component
inverse,  based on a simple time reversal, has been introduced. The
sample  configuration files have been rewritten to take advantage of the
new  inversion procedure. Sample configuration files for 48 KHz, 88.2
KHz, 96  KHz sample rates have been added. The homomorphic deconvolution
 procedure has been improved to avoid any numerical instability. A new 
Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation 
method, providing monotonic behaviour, has been introduced in the target
 response computation. All the interpolation and approximation
procedures  have been rewritten from scratch to provide better
performances and  accuracy.
  

3.2.4  Version 2.6.2
--------------------
  
  A new command line parameters replacement functionality has been
introduced. The dip and peak limiting procedures have been improved in
order to avoid numerical instabilities. A new wavelet based analysis
graph has been added to the sample results. Many performance
improvements have been introduced. A new optional parameter used to
define the base directory for all files has been added.
  

3.2.5  Version 2.6.1
--------------------
  
  Minor corrections and improvements have been applied to the
documentation and to the pre-echo truncation inversion procedure. A new
target transfer function definition procedure based on Uniform B Splines
has been introduced. The development environment has been moved to
Code::Blocks and GCC/MinGW.
  

3.2.6  Version 2.6.0
--------------------
  
  A new prefiltering curve based on the bilinear transformation has been
introduced. An improved windowing of the minimum phase filters used to
apply the target frequency response and the microphone compensation has
been implemented. A missing normalization of the minimum phase
correction filter has been added. A new logarithmic interpolation has
been added to the target transfer function computation. The new
interpolation method simplifies the definition of the target transfer
functions. Small improvements to the documentation and to the Octave
scripts used to generate the graphs have been applied. A new improved
version of the measurejack script has been included in the package. Some
new sample configuration files, including one approximating the ERB
psychoacoustic scale, have been added.
  

3.2.7  Version 2.5.1
--------------------
  
  Small improvements to the documentation and to the Octave scripts used
to generate the graphs. The sliding lowpass prefiltering procedure has
been rewritten to make it a bit more accurate and to make the code more
readable. Few other minor bugs have been fixed.
  

3.2.8  Version 2.5.0
--------------------
  
  With version 2.5.0 a general overhauling of the filter generation
procedure has been performed. Some steps (peak limiting for example)
have been moved to a different stage of the procedure, and new stages
have been added. 
  A new ringing truncation stage has been added to remove excessive
ringing caused sometimes by the pre-echo truncation procedure. Now the
filter impulse response is enclosed in a sort of psychoacoustic jail
that prevent, or at least reduces a lot, any artifact that could arise
as a side effect of the filter generation procedure. With this changes
DRC becomes somewhat "self tuning" and now it is able to adapt itself to
the input impulse response, at least to some extent, providing as much
correction as possible without generating excessive artifacts.
  The postfiltering stage, where the target transfer function is
defined, has been split to provide a separate stage for microphone
compensation. This allows for a greater flexibility defining both the
target transfer function and the microphone compensation, and provides
as a side effect correct test convolutions even when microphone
compensation is in place. With the previous versions the test
convolution was improperly altered by the microphone compensation,
because both the target transfer function and the microphone
compensation were generated and applied using the same filter.
  Many other procedures have been refined. For example the peak and dip
limiting procedures now ensure continuity up to the first derivative of
the magnitude response on the points where the magnitude limiting starts
its effect. This further reduces the ringing caused by abrupt changes in
the magnitude response. 
  Finally many other minor bugs have been corrected and the
documentation has been improved, switching to LaTeX for document
generation and formatting.
  

3.2.9  Version 2.4.2
--------------------
  
  Version 2.4.2 added a better handling of underflow problems during
homomorphic deconvolution. Some little speed improvements have been also
achieved. Added search and output of peak value and peak position into
lsconv.
  

3.2.10  Version 2.4.1
---------------------
  
  Version 2.4.1 added some tools for accurate time aligned impulse
response measurements. This make it possible to compensate for
interchannel misalignments, at least up to a limited extent. Some minor
bugs have been also corrected.
  

3.2.11  Version 2.4.0
---------------------
  
  In version 2.4.0 the Takuya Ooura and GNU Scientific Library FFT
routines have been included in the program. These routines are about 10
times faster than the previous routines, providing about the same
accuracy. Furthermore some checks have been added to the sharpness
parameters to avoid program crashes when these parameters are missing.
  The FFT routines described above are available at:
    http://www.gnu.org/software/gsl/
   http://www.kurims.kyoto-u.ac.jp/~ooura/fft.html 
  
  

3.2.12  Version 2.3.2
---------------------
  
  In version 2.3.2 a new sharpness factor parameter has been added to
the sliding low pass prefiltering procedure. This parameter provides a
control between filtering sharpness and spectral spreading in the filter
transition region. A new option to read and write double precision
floating points files has been added. Some checks to warn when the input
signal is too short to provide accurate results has been added.
  

3.2.13  Version 2.3.1
---------------------
  
  In version 2.3.1 some minor corrections to the program have been
performed and the documentation has been restructured. A new option to
automatically count the number of lines in the target function and
microphone compensation files has been added. A new optimized sample
configuration file has been added.
  

3.2.14  Version 2.3.0
---------------------
  
  Version 2.3.0 adds two parameters to control the gain limiting
procedures. These parameters control a sort of "soft clipping" of the
frequency response, avoiding ringing on abrupt truncations of the
frequency response. A new parameter to select the magnitude type, either
linear or expressed in dB, of the target frequency response has been
added. The optional capability to perform microphone compensation has
also been added. The license has been switched to the GNU GPL.
  

3.2.15  Version 2.2.0
---------------------
  
  Version 2.2.0 added a sliding low pass procedure to the pre-echo
truncation inversion procedure. This pre-echo truncation procedure is
much more similar to the pre-echo sensitivity of our hear and so
slightly better results are achieved. Furthermore the sliding low pass
prefiltering procedure has been completely rewritten to provide better
accuracy, especially with the short window lengths needed for pre-echo
truncation.
  

3.2.16  Version 2.1.0
---------------------
  
  Version 2.1.0 added two new parameters that allow for the windowing of
everything coming more than few samples before the impulse center.
Usually before the main spike there's only noise and spuriae. I have
found that in certain situations this small noise may lead to audible
errors in the correction, so windowing it out in order to clean the
impulse response is a good practice.
  

3.2.17  Version 2.0.0
---------------------
   
  Version 2.0.0 added many new features that provides much better
control on pre-echo artifacts problems. The most important change is the
new pre-echo truncation inversion procedure. Loosely derived from
Kirkeby fast deconvolution this new procedure truncates any pre-echo on
the excess phase part inversion. This leads to something like minimum
phase inversion on frequency ranges where a complete inversion would
lead to pre-echo artifacts. This critical frequency ranges are usually
no more than 5 or 6 and no wider than about 1/12 of octave for a typical
room impulse response. Reducing the correction to minimum phase on so
narrow bands has little or no subjective effect on the correction
quality and allows for the correction of much longer windows, with much
better overall results.
  Avoiding pre-echo artifacts also provides the ability to create low
input-output delay filters. The resulting delay is often low enough (few
ms) to allow the use of these filters in home theater applications. For
situations where even few ms aren't adequate there's now also an option
to generate zero delay minimum phase filters. Minimum phase filters
provides correction of the amplitude response and just the minimum phase
part of the phase response.
  In order to avoid pre-echo artifacts there are also many other aspects
that should be taken into account. For a better explanation of the whole
procedure and the selection method for the DRC parameters needed to
achieve this result look at the section 4.6.1. 
  Version 2.0.0 adds also many other improvements, including the single
side version of the prefiltering procedures and fixing for many minor
bugs that where still laying around.
  A test convolution stage is now also available. This convolves the
input impulse response with the generated filter to get the impulse
response after correction. The impulse response obtained by this method
is usually really reliable. As long as the measurement microphone isn't
moved I have been able to verify the computed impulse response with less
than 0.5 dB errors, which is impressive considering the cheap
measurement set I use. In my situation may be that the computed
corrected impulse response is even more accurate than the measured one,
because of noise problems being doubled by my cheap measurement set in
the second measure.
  

3.2.18  Version 1.3.0
---------------------
  
  Version 1.3.0 provided some new features with respect to version
1.2.1:
  
 
 
   - More flexible prefiltering curve parameters
 
   - New time varying sliding lowpass prefiltering stage
 
   - New minimum phase or homomorphic renormalization of the prefiltered
   excess phase component
 
   - Homomorphic deconvolution based on the Hilbert transform instead of
   the cepstrum method
 
   - Slightly improved documentation
 
   - Many minor bugs fixed
  
  

4  Program description and operation
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=

  
  DRC is a program used to generate correction filters for acoustic
compensation of HiFi and audio systems in general, including listening
room compensation. DRC generates just the FIR correction filters, which
must be used with a real time or offline convolver to provide real time
or offline correction. DRC doesn't provide convolution features, and
provides only some simplified, although really accurate, measuring
tools. So in order to use DRC you need:
  
 
 
   1. At least 1 second of the impulse response of your room and audio
   system at the listening position, separated for each channel, which
   means usually just left and right for a basic HiFi system. The
   impulse response should be provided in raw format (flat file with
   just samples, no headers or additional information whatsoever),
   either in signed 16 bit format or using 32/64 bit IEEE floating point
   samples. From version 2.4.1 DRC includes some command line tools to
   do accurate time aligned impulse response measurement, see section
   4.4 for further details. Many other systems, either commercial or
   free, are available on the Internet to carry out this task. Take a
   look at:
 
     
      - Room Eq Wizard http://www.hometheatershack.com/roomeq/ 
      - rec_imp:
      http://www.duffroomcorrection.com/wiki/Simple_Automated_IR_Measuri
      ng_Tool  
      - ETF: http://www.etfacoustic.com/ 
      - Sample Champion: http://www.purebits.com/ 
      - Aurora plugins: http://www.aurora-plugins.com/ 
      - MLSSA: http://www.mlssa.com/ 
      - CLIO: http://www.audiomatica.it/ 
      - Audua Speaker Workshop: http://www.speakerworkshop.com/ 
      - The MLS system provided with the Nwfiir Audio Tools suite 
      - LAUD 
      - Techron TEF 
  Since some time there are also some integrated packages provinding
   both  the measurements functionality and the correction, based on
   DRC. Some  examples: 
 
     
      - Align: http://www.ohl.to/about-audio/audio-softwares/align/ 
      - The Final Cut:
      http://www.ohl.to/about-audio/audio-softwares/the-final-cut/ 
      - Inguz Audio: http://inguzaudio.com/ 
  This packages may be really useful, expecially for unexperienced
   peoples.
 Many information and free programs useful for measuring and handling
   impulse responses are available at the NoiseVault web site:
       http://www.noisevault.com/ 
  Of course a good instrumentation microphone and preamplifier are
   needed to get accurate measurements of your listening room response.
   The ETF web sites has a link to a cheap but still quite good
   instrumentation microphone, which comes with an individual
   calibration file:
       http://www.ibf-akustik.de/ 
 
 It is built around the Panasonic electrect capsules (WM-60A and WM-61A)
    which can be used also to build a DIY microphone. Of course you
   won't  get the same quality of a professional instrumentation
   microphone, but  it is enough to get good results. Another good and
   inexpensive solution  is the Behringer ECM8000 measurement microphone
   (see  http://www.behringer.com for details). 
 
   2. A real time convolver able to deal with FIR filters with at least
   4000 and up to more than 32000 taps, like BruteFIR, Foobar2000, the
   ActiveX Convolver Plugin and others. References for these programs
   can be found at the following links:
  
     
      - BruteFIR: http://www.ludd.luth.se/~torger/brutefir.html 
      - ActiveX Convolver Plugin: http://convolver.sourceforge.net 
      - Foobar2000 with convolver plugin: http://www.foobar2000.org/ 
      - Jconv: http://www.kokkinizita.net/  
      - ACXO: http://pcazeles.perso.cegetel.net/acxo.htm 
      - RealReverb WinAmp plugin, optionally along with the LineIn
      plugin: 
          http://www-personal.umich.edu/~mressl/
         	 http://www.winamp.com/
         http://home.hccnet.nl/th.v.d.gronde/ 
     
      - SIR Reverb plugin: http://www.knufinke.de/sir/index_en.html 
      - Aurora plugins: http://www.aurora-plugins.com/ 
      - CATT FIReverb suite: http://www.catt.se/the_suite.htm 
      - Convo Boy: http://www.kvraudio.com/get/1469.html 
      - Voxengo Pristine Space: http://www.voxengo.com/product/pspace/
  Furthermore a ready to use Linux distribution suited for audio
   applications is available at Planet CCRMA:	
       http://ccrma-www.stanford.edu/planetccrma/software/ 
  This distribution already contains most of what is needed to create a
   real time convolution engine suited for digital room correction.
 On the DRC Wiki pages created by Ed Wildgoose there's a document,
   created by Uli Brueggemann, on how to create a Linux mini
   distribution suited to run BruteFIR out of a USB memory stick. Take a
   look at: 	 
       http://www.duffroomcorrection.com/ 
  and search for "BruteFIR on a USB memory stick". Further informations
   about  this option are available on the Acourate web site:
       http://www.acourate.com/ 
 
 
   3. Hardware needed to run all the programs. I'm actually using a 
   "Shoe Box" PC manufactured by ITOX (http://www.itox.com) along  with
   a TerraTec EWX 24/96 sound card. This "Shoe Box" PC is running  Linux
   (RedHat 7.3), ALSA (see http://www.alsa-project.org) and  BruteFIR to
   provide real time correction from the optical S/PDIF output  of a
   consumer CD player. The PC configuration is really simple (Intel 
   Celeron CPU running at 800 MHz, 64 Mb of RAM, old 1.6 Gb Hard Disk)
   but  it is more than adequate for real time correction of two
   channels  running at 44.1 KHz. With this configuration BruteFIR uses
   just about  15% of the CPU power. 
 Of course to test the program you can also apply the correction
   off-line  on audio files ripped from ordinary audio CDs, burning the
   corrected  files on some fresh CDR and listening to them using a
   standard CD  player. This avoids the need of any dedicated hardware
   and lets you test  DRC on your favourite CD player. 
 Since few years there are many good, silent and compact PCs designed
   for  multimedia usage which could be used to build a complete
   noiseless real  time convolver with little effort. For some examples
   take a look at: 
       http://www.cappuccinopc.com/
      http://www.stealthcomputer.com/
      http://www.tranquilpc.co.uk/
      http://www.mini-itx.com/
      http://www.hushtechnologies.com/ 
 
  
  

4.1  Filter generation procedure
================================
  
  The creation of a correction filter for room acoustic compensation is
quite a challenging task. A typical acoustic environment is a non
minimum phase system, so in theory it cannot be inverted to get perfect
compensation. Furthermore a typical HiFi system in a typical listening
room isn't either a single linear system, but it is instead a different
linear system for every different listening position available.
  Trying to get an almost perfect compensation for a given position
usually leads to unacceptable results for positions which are even few
millimeters apart from the corrected position. The generation of a
filter that provides good compensation of magnitude and phase of the
frequency response of the direct sound, good control of the magnitude of
the frequency response of the stationary field and an acceptable
sensitivity on the listening position, requires many steps. Here it is a
brief summary of what DRC does:
  
 
 
   1. Initial windowing and normalization of the input impulse response.
 
   2. Optional microphone compensation.
 
   3. Initial dip limiting to prevent numerical instabilities during
   homomorphic deconvolution.
 
   4. Decomposition into minimum phase and excess phase components using
   homomorphic deconvolution.
 
   5. Prefiltering of the minimum phase component with frequency
   dependent windowing.
 
   6. Frequency response dip limiting of the minimum phase component to
   prevent numerical instabilities during the inversion step.
 
   7. Prefiltering of the excess phase component with frequency
   dependent windowing.
 
   8. Normalization and convolution of the preprocessed minimum phase
   and excess phase components (optional starting from version 2.0.0).
 
   9. Impulse response inversion through least square techniques or fast
   deconvolution.
 
   10. Optional computation of a psychoacoustic target response based on
   the magnitude response envelope of the corrected impulse response.
 
   11. Frequency response peak limiting to prevent speaker and
   amplification overload.
 
   12. Ringing truncation with frequency dependent windowing to remove
   any unwanted excessive ringing caused by the inversion stage and the
   peak limiting stage.
 
   13. Postfiltering to remove uncorrectable (subsonic and ultrasonic)
   bands and to provide the final target frequency response.
 
   14. Optional generation of a minimum phase version of the correction
   filter.
 
   15. Final optional test convolution of the correction filter with the
   input impulse response.
   Almost each of these steps have configurable parameters and the
optional capability to output intermediate results.
  Of course I'm not sure at all that this is the best procedure to get
optimal correction filters. There is a lot of psychoacoustic involved in
the generation of room acoustic correction filters, so probably the use
of a more psychoacoustic oriented procedure would give even better
results. Any suggestion with respect to this is appreciated.
  Within my HiFi system the application of the correction provides huge 
improvements. By the way my system no longer can be considered a normal 
HiFi system. It is actually much closer to a studio monitoring system 
placed in a heavily damped room. Furthermore there is also an high 
performance subwoofer, extending the response down into the infrasonic 
range, and everything has been tuned to provide the best results with 
the correction in place. For some example of the results achieved see 
appendix A. 
  

4.2  Frequency dependent windowing
==================================
   
  The frequency dependent windowing is one of the most common operations
within DRC. This type of windowing follow up directly from the fact that
within a room the sensitivity of the room transfer function to the
listening position is roughly dependent on the wavelength involved. This
of course implies that the listening position sensitivity increase quite
quickly with frequency.
  This dependence has the side effect that the room correction need to
be reduced as the frequency increase, or, seen from the other side, as
the wavelength decrease. For this reason DRC tries to apply a correction
that is roughly proportional to the wavelength involved. This approach
has also some psychoacoustic implications, because our auditory system
is conceived to take into account the same exact room behaviour, and so
its own behaviour follow somewhat similar rules.
  Within DRC the frequency dependent windowing is implemented with two 
different kind of procedures: band windowing and sliding lowpass linear 
time variant filtering. The first procedure simply filters the input 
signals into logarithmically spaced adjacent bands and applies different
 windows to them, then summing the resulting signals together to get the
 output windowed impulse response. The second procedure uses a time 
varying lowpass filter, with a cut-off frequency that decreases with the
 window length. The results are pretty similar, but usually the sliding 
lowpass procedure is preferred because it is less prone to numerical 
errors and allows for a bit more of flexibility. 
  Both procedures follow the same basic rules in order to define the
type of windowing that gets applied to the input signal. The basic
parameters are the lower window, i.e. the window applied at the lower
end of the frequency range involved, the upper window, i.e. the window
applied at the upper end of the frequency range, and the window
exponent, i.e. the exponent used to connect the lower window to the
upper window with a parametric function that goes as the inverse of the
frequency. For a description of the parametric function used see section
6.4.8.
        --------------------------------------------------------
   
          [width=0.9@percent,keepaspectratio]figures/DBP-Linear 
  Figure 1:  Frequency dependent windowing for the normal.drc sample
settings on the time-frequency plane. Linear scale. The X axis is time
in milliseconds, the Y axis is frequency in Hz. The part that gets
corrected is the one below the windowing curves.
                                     
   
        --------------------------------------------------------
  
  For example figure 1 show the typical set of  prefiltering curves
applied to the input impulse response by the  normal.drc sample settings
(see section 5.2).  For this sample settings file the default setting
for the window  exponent, which is the WE parameter in the figure, is
1.0. The part of  the input impulse response that is preserved, and so
also corrected, is  the one below the curves. The remaining part of the
time-frequency plane  is simply windowed out and ingored in the
correction.
  Looking at this figure it becomes pretty clear that only a tiny
fraction of the time-frequency plane gets corrected by DRC. This tiny
fraction pretty much defines the physical limits where digital room
correction is applicable. Above this limit the listening position
sensitivity usually becomes so high that even a small displacement of
the head from the optimal listening position causes unacceptable results
with the appearance of strong audible artifacts.
        --------------------------------------------------------
   
         [width=0.9@percent,keepaspectratio]figures/DBP-SemiLogY 
  Figure 2:  Frequency dependent windowing for the normal.drc sample
settings on the time-frequency plane. Logarithmic frequency scale. The X
axis is time in milliseconds, the Y axis is frequency in Hz.
                                     
   
        --------------------------------------------------------
  
  By the way it should be also taken into account that our ear perceives
this time-frequency plane on a logarithmic frequency scale. Looking at
the same graph on a logarithmic frequency scale, as in figure 2, it
becomes clear that from our auditory system point of view a much bigger
fraction of the time-frequency plane gets corrected. It becomes also
clear that above 1-2 KHz only the direct sound gets corrected and that
above that range room correction actually reduces to just minimalistic
speaker correction.
        --------------------------------------------------------
   
         [width=0.9@percent,keepaspectratio]figures/DBP-SemiLogX 
  Figure 3:  Frequency dependent windowing for the normal.drc sample
settings on the time-frequency plane. Logarithmic time and linear
frequency scales. The X axis is time in milliseconds, the Y axis is
frequency in Hz.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
          [width=0.9@percent,keepaspectratio]figures/DBP-LogLog 
  Figure 4:  Frequency dependent windowing for the normal.drc sample
settings on the time-frequency plane. Logarithmic time and frequency
scales. The X axis is time in milliseconds, the Y axis is frequency in
Hz.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
           [width=0.9@percent,keepaspectratio]figures/DBP-Gabor 
  Figure 5:  Frequency dependent windowing for the normal.drc sample
settings on the time-frequency plane. Logarithmic time and frequency
scale with Gabor limit superimposed. The X axis is time in milliseconds,
the Y axis is frequency in Hz.
                                     
   
        --------------------------------------------------------
  
  While developing DRC I've read some informal notes on the Internet 
stating that on short time windows our perception of time should be 
considered on a logarithmic scale too. I'm not quite convinced that this
 assumption is actually true, but if such an assumption is correct our 
perception of the room correction would be as in figures  3 and 4. Even
if this  assumption is not true these graphs are pretty useful to make
clearly  visible the part of the time-frequency plane that gets
corrected by DRC  and becomes even more useful if also the Gabor limit
is placed in the  graph as in figure 5. 
  The Gabor limit is defined by the following simple inequality: 	 
                                            1 
                         	Delta f Delta t > - 
                                            2 
   where f is frequency and t is time, and defines the limit of 
uncertainity in the time-frequency plane. This means for example that, 
looking at picture 5, when the window exponent goes below  about 0.5 the
frequency dependent windowing starts violating the Gabor  inequality at
least in some small frequency range. Within that range the  room
transfer function estimation performed by DRC becomes inaccurate  and
the room correction might be affected by appreciable errors in the 
evaluation of the room transfer function.
        --------------------------------------------------------
   
       [width=0.9@percent,keepaspectratio]figures/DBP-BPComparison 
  Figure 6:  Comparison between the standard proportional windowing
curve and the new one based on the bilinear transformation. Logarithmic
time and frequency scale. The X axis is time in milliseconds, the Y axis
is frequency in Hz.
                                     
   
        --------------------------------------------------------
  
  Starting with version 2.6.0 a prefiltering curve based on the bilinear
transform has been introduced. This curve provides a better match with
the typical resolution of the ear and also with the typical behaviour of
the listening room. The windowing curve provides the same exact results
as the previous windowing curve when the window exponent is set to 1.0,
but provides a different behaviour when the window exponent is changed,
as showed in figure 6. The closer approximation of the ear behaviour is
clearly visible in figure 8, where it is shown that using an appropriate
configuration of the windowing parameters it is possible to get a close
to perfect match with the ERB psychoacoustic scale (see curves labeled
ERB and erb.drc, which overlap almost perfectly).
  

4.2.1  Pre-echo truncation
--------------------------
   
  Starting from version 2.7.0 this step is implicitely disabled. 
Considering that excess phase inversion is performed simply by time 
reversal of the excess phase component, pre-echo is implicitely limited 
by the frequency dependent windowing performed on the excess phase. The 
description of this step and the code performing it has been retained 
because it could be used for experimental reasons, especially 
considering that the reequalization to flat performed in this step is 
time reversed with respect to that performed in the excess phase 
pre-processing. This meas that a minimum phase reequalization performed 
in the pre-echo truncation is equivalent to a maximum phase 
reequalization in the excess phase pre-processing, and the other way 
around. 
  If enabled frequency dependent windowing is used to truncate the 
pre-echo caused by the inversion of the excess phase part of the impulse
 response. The truncation procedure is always the same but it is 
implicitely applied on the left side of the time-frequency plane instead
 of the right side, because inversion of the excess phase corresponds to
 a time reversal. A much shorter windowing is used because our ear is 
quite sensitive to pre-echo. 
  Windowing out part of the impulse response of the excess phase
component  of the correction filter of course makes it no longer an
all-pass  filter, i.e. the excess phase part no longer has a flat
magnitude  response. To compensate for this problem the excess phase
component  magnitude response is equalized back to flat using, after
inversion, a  minimum phase filter. This of course causes some
post-ringing. Even  though this usually happens only on few narrow
bands, it might be quite  audible, and gets limited by the subsequent
ringing truncation stage. 
  

4.2.2  Ringing truncation stage
-------------------------------
   
  Since version 2.5.0 a further frequency dependent windowing is applied
 directly to the filter after impulse response inversion and peak 
limiting. This is performed to remove any residual ringing caused by the
 previous steps, especially the dip and peak limiting steps, even though
 this implies some tradeoff on filter accuracy. 
        --------------------------------------------------------
   
           [width=0.9@percent,keepaspectratio]figures/DBP-Jail 
  Figure 7:  Frequency dependent windowing jail for the normal.drc
sample settings on the time-frequency plane. Linear time scale and
logarithmic frequency scale. The X axis is time in milliseconds, the Y
axis is frequency in Hz.
                                     
   
        --------------------------------------------------------
  
  With this further step the filter impulse response gets enclosed in a 
sort of time-frequency jail defined by the excess phase windowing 
settings on the left side of the time-frequency plane and by the ringing
 truncation settings on the right side (see figure 7).  Considering that
this time-frequency bounds have also some  psychoacoustic implications,
with this time-frequency enclosure DRC  should be able to truncate
automatically any part of the correction that  is probably going to
cause audible artifacts. Following this lines DRC  gains at least a bit
of psychoacoustically based "self tuning" and  should become more robust
and less prone to artifacts. 
        --------------------------------------------------------
   
         [width=0.9@percent,keepaspectratio]figures/DBP-BWidthCmp 
  Figure 8:  Resolution bandwidth, as a function of frequency, for the
frequency dependent windowing and various standard smoothing procedures,
including the Bark and ERB psychoacoustic scales. The X axis is
frequency in KHz, the Y axis is frequency in Hz, both plotted on a
logarithmic scale. The windowing parameters of the normal.drc and
erb.drc sample settings files have been used to plot the DRC resolution
curves.
                                     
   
        --------------------------------------------------------
  
  Applying the Gabor inequality to the window length between the two
curves of pre-echo and ringing truncation it is pretty easy to get an
equivalent frequency resolution, as a function of center frequency, of
the frequency dependent windowing procedure. This resolution could be
compared, as in figure 8, to some standard smoothing procedures widely
used within many audio applications, like fractional octave smoothing
and the classical Bark and ERB psychoacoustic scales.
  From figure 8 it is pretty clear that the correction resolution used
by DRC is well above that of any of the standard smoothing procedures,
at least with the normal.drc sample settings file (see section 5.2).
This means that the correction should provide a perceived frequency
response that is really close to the configured target frequency
response.
  The "erb.drc" resolution plot show the approximation of the ERB scale
provided by the "erb.drc" sample settings file (see section 5.2. The
approximation has been created assuming:
                         	Delta f Delta t = 2 
   instead of the usual Gabor inequality (see figure 5), i.e.  assuming
that the frequency dependent windowing with the settings used  has a
resolution that is about four times above the Gabor limit. This is  a
rough estimate of the true resolution achieved by the DRC procedure in 
this situation. This estimation has been derived considering the 
compound effect of the various overlapped windows applied at various 
stages of the filter generation procedure. 
  

4.3  Psychoacoustic target computation
======================================
   
  Starting from version 3.0.0 an optional stage, used to compute a
target  frequency response based on the psychoacoustic perception of the
 corrected frequency response, has been introduced. The target response 
is based on the computation of the magnitude response envelope of the 
corrected impulse response, which is an extension of the spectral 
envelope concept. This is performed before the application of the usual 
target response, so that the standard target response is not compensated
 back by this stage.
  The spectral envelope is a concept which has been introduced in the 
field of speech synthesis and analysis and is defined simply as a smooth
 curve connecting or somewhat following the peaks of the signal
spectrum.  There are strong arguments and experimental evidence
supporting this  approach and the idea that our ear uses the spectral
envelope for the  recognition of sounds. The spectral envelope, for
example, allow our ear  to understand speech under many different
conditions, whether it is  voiced, whispered or generated by other
means. These different  conditions generate completely different
spectrums but usually pretty  similar spectral envelopes. The spectral
envelope also easily explains  why our ear is more sensitive to peak in
the magnitude response and less  sensitive to dips. A curve based on the
peaks of the magnitude response  is by definition little or not affected
at all by dips in the frequency  response. 
  In the speech recognition field many procedures have been developed to
 compute the spectral envelope. Some of them are based on Linear 
Predictive Coding (LPC), the Discrete Cepstrum, the so called "True 
Envelope" and finally the Minimum Variance Distortionless Response 
(MVDR). Most of these methods are optimized for speed, noise resilience 
and to provide good results in the voice spectrum range sampled at low 
sample rates, so they are not really suited for HiFi usage. 
  Within DRC a different procedure has been developed. This is a
variation  of the usual fractional octave smoothing procedure, using the
parametric  Holder mean instead of the usual simple averaging.
Furthermore the  smoothing has been extended to provide the Bark and ERB
scales  resolution when applicable. 
        --------------------------------------------------------
   
     [width=0.9@percent,keepaspectratio]figures/DBP-SpectralEnvelope 
  Figure 9:  Example of a magnitude response envelope. The  unsmoothed
magnitude response of a typical room, corrected with a flat  target, is
plotted. Superimposed there is the usual smoothing, computed  on the ERB
scale, showing an essentially flat magnitude response, as  expected. The
magnitude response envelope, computed on the ERB scale too using 
standard parameters, show a rising slope which is in good agreement with
 the inverse of one of the target responses suggested in the literature.
                                      
   
        --------------------------------------------------------
  
  For the tuning of the parameters used in the magnitude response
envelope  computation some typical real world room magnitude responses
have been  taken. The computation parameters have been set so that the
resulting  magnitude response envelope provides a target response as
close as possible to the  inverse of the usual target responses
suggested in the literature. An  example is reported in picture 9. The
same  parameters have been tested also in some not so common room to
check  that they were still providing the expected results. Of course, 
considering that now the basic target response is provided by the 
inverse of the magnitude response envelope, the usual target responses
are no  longer needed, apart from subsonic or ultrasonic filtering, and
should  be set to flat. For this reason the flat response is now the
default  target for all standard configuration files. The standard
target  response stage should be used only to adjust the response to
taste, but,  unlike previous versions, for a neutral reproduction a flat
response  should be used. 
  From the subjective point of view a system equalized to the inverse of
 the magnitude response envelope usually sound really neutral. Even
though most of  the times the magnitude response envelope response is
different among the various  channels, resulting in an obvious channel
misalignement if evaluated  with the standard smoothing procedures,
imaging usually improves,  becoming more stable and focused. This appear
to confirm that the  estimation performed by the magnitude response
envelope has to be close to  the subjective perception of the magnitude
response. 
  

4.4  Impulse response measurement
=================================
   
  Starting from version 2.4.1 two simple command lines tools, glsweep
(Generate Log Sweep) and lsconv (Log Sweep Convolution), are available
to perform accurate time aligned impulse response measurements. These
tools are based on the log sweep method for impulse response
measurement, which is one of the most accurate, especially for acoustic
measurements. This method is based on a special signal, which is a
logarithmic sinusoidal sweep, that need to be reproduced through the
system under test, and an inverse filter, which, when convolved with the
measured log sweep, gives back the impulse response of the system.
  The steps needed to get the impulse response are the following:
  
 
 
   1. Generate the log sweep and inverse filter using glsweep,
   optionally converting the sweep to a suitable format.
 
   2. Play the log sweep through your system using a soundcard while
   recording the speaker output using a (hopefully good) microphone and
   any recording program. 
 
   3. Convolve the recorded log sweep with the inverse filter using
   lsconv to get the final impulse response.
   If full duplex is supported by the soundcard, recording may be
performed using the same soundcard used for playing. Using two different
soundcards or a CD Player for reproduction and a soundcard for recording
usually provides worse results unless they are accurately time
synchronized.
  The lsconv tool allows also for the use of a secondary reference
channel to correct for the soundcard frequency response and for any time
misalignment caused by the soundcard itself, the soundcard drivers or
the play and recording programs. This soundcard compensation of course
works if the reference channel has the same behaviour of the measuring
channel. The typical use of this feature would be the use of one channel
of a stereo or multichannel soundcard to measure the system and another
one used in a loopback configuration to get the reference channel needed
to correct the soundcard itself.
  With this configuration even with cheap soundcards it is pretty easy
to get a  +/- 0.1  dB frequency response over the audio frequency range
with near to perfect time alignment and phase response. Considering that
the log sweep method ensure by itself a strong noise rejection (90 dB of
S/N ratio is easily achievable even in not so quiet environments) and a
strong rejection to artifacts caused by the system non linear
distortions, with this method the final measurements usually have true
state of the art accuracy.
  Finally an important warning: playing the log sweep signal at an
excessive level can easily damage your speakers, especially the
tweeters. So be really careful when playing such a signal through your
equipment. The "Jones Rush" guide (see section 1) provides some useful
hints to help you in the use of this kind of tools without the risk of
damaging your equipment. No responsibility is taken for any damage to
your equipment, everything is at your own risk.
  

4.4.1  The glsweep program
--------------------------
  
  When executed without parameters the glsweep program gives the
following output:
    
   <<GLSweep 1.0.2: log sweep and inverse filter generation.
     Copyright (C) 2002-2005 Denis Sbragion
     
     Compiled with single precision arithmetic.
      
     This program may be freely redistributed under the terms of
     the GNU GPL and is provided to you as is, without any warranty
     of any kind. Please read the file "COPYING" for details.
     
     Usage: glsweep rate amplitude hzstart hzend duration silence
             leadin leadout sweepfile inversefile
     
     Parameters:
     
       rate: reference sample rate
       amplitude: sweep amplitude
       hzstart: sweep start frequency
       hzend: sweep end frequency
       duration: sweep duration in seconds
       silence: leading and trailing silence duration in seconds
       leadin: leading window length as a fraction of duration
       leadout: trailing window length as a fraction of duration
       sweepfile: sweep file name
       inversefile: inverse sweep file name
      
     Example: glsweep 44100 0.5 10 21000 45 2 0.05 0.005 sweep.pcm
   inverse.pcm
   >>
    
   The program output contains some brief explanation of the generation 
parameters and some sample options.
  The longer the log sweep used the stronger the noise rejection of the
measure. A 45 seconds log sweep usually gives more than 90 dB of signal
to noise ratio in the final impulse response even when used in somewhat
noisy environments, for example one where the computer used to do the
measure is in the same room of the measured system, producing all of its
fan noise. The output format is the usual raw file with 32 bit IEEE
floating point samples. If you need to convert the sweep generated using
the example above to a 16 bit mono WAV file you can use SoX with a
command line like this one:
    
   <<sox -t f32 -r 44100 -c 1 sweep.pcm -t wav -c 1 sweep.wav
   >>
    
   SoX, can be downloaded at:
    http://sox.sourceforge.net/ 
   If you want to create a stereo WAV file to get also the reference
channel you can use something like:
    
   <<sox -t f32 -r 44100 -c 1 sweep.pcm -t wav -c 2 sweep.wav
   >>
    
   The inverse filter doesn't need to be converted to a WAV file because
lsconv is already able to read it as is. If you need to convert a
recorded sweep stored in a wav file back to a raw 32 bit floating point
format use this command:
    
   <<sox recorded.wav -t f32 recorded.pcm
   >>
    
   If you have a stereo WAV file with both the measurement channel and
the reference channel you can extract them into two files using:
    
   <<sox recorded.wav -t f32 -c 1 recorded.pcm mixer -l
     sox recorded.wav -t f32 -c 1 reference.pcm mixer -r
   >>
    
   provided that the recorded channel is the left one ("mixer -l"
parameter) and the reference channel is the right one ("mixer -r"
parameter).
  

4.4.2  The lsconv program
-------------------------
  
  When executed without parameters the lsconv program gives the
following output:
    
   <<LSConv 1.0.3: log sweep and inverse filter convolution.
     Copyright (C) 2002-2005 Denis Sbragion
     
     Compiled with single precision arithmetic.
     
     This program may be freely redistributed under the terms of
     the GNU GPL and is provided to you as is, without any warranty
     of any kind. Please read the file "COPYING" for details.
      
     Usage: LSConv sweepfile inversefile outfile [refsweep mingain
   [dlstart]]
      
     Parameters:
      
       sweepfile: sweep file name
       inversefile: inverse sweep file name
       outfile: output impulse response file
       refsweep: reference channel sweep file name
       mingain: min gain for reference channel inversion
       dlstart: dip limiting start for reference channel inversion
     
     Example: lsconv sweep.pcm inverse.pcm impulse.pcm refchannel.pcm
   0.1 0.8
   >>
    
   All files must be in the usual raw 32 bit floating point format. To
get the impulse response without the use of a reference channel just use
something like:
    
   <<lsconv recorded.pcm inverse.pcm impulse.pcm
   >>
    
   Where "recorded.pcm" is the recorded sweep, "inverse.pcm" is the
inverse filter generated by glsweep and "impulse.pcm" is the output
impulse response ready to be fed to DRC.
  If you also want to use the reference channel use something like:
    
   <<lsconv recorded.pcm inverse.pcm impulse.pcm reference.pcm 0.1
   >>
    
   The "0.1" value is the minimum allowed gain for the reference channel
inversion. 0.1 is the same as -20 dB, i.e. no more then 20 dB of the
reference channel frequency response will be corrected. This is needed
also to prevent numerical instabilities caused by the strong cut off
provided by the soundcard DAC and ADC brick wall filters.
  When used with the reference channel the main spike of the impulse
response is always at exactly the same length of the log sweep used,
provided that the two soundcard channels are perfectly synchronized. Of
course this is usually true for all soundcards.
  For example if a 10 seconds sweep is used the main spike will be
exactly at 10 seconds from the beginning of the output impulse response,
i.e. at sample 441000 if a 44.1 KHz sample rate is used.
  If the main spike is at a different position it means that there's
some delay in the measurement channel, usually caused by the time the
sound takes to travel from the speaker to the microphone. If this delay
is different for different channels it means that there's a time
misalignment between channels that needs to be corrected. Up to a
limited amount, and using some small tricks, DRC is already able to
compensate for interchannel delays (see section 4.6.5). Some future DRC
release will include better support for interchannel time alignment.
  

4.4.3  Sample automated script file
-----------------------------------
  
  Under the "source/contrib/Measure" directory of DRC there's a sample
Linux shell script, called "measure", that uses glsweep, lsconv, SoX and
standard ALSA play and recording tools to automate the time aligned
measurement procedure using a reference channel. This sample script can
be used only under Linux and it is just a quick hack to allow expert
users to automate the whole procedure. Use it at your own risk.
  Furthermore this script has been developed with an old version of SoX 
(12.17.7) so it might need some changes to work with more recent 
versions. It also needs any related tools ready to be executed from the 
working directory, else it doesn't work. When executed without 
parameters the script gives the following output: 
    
   <<Automatic measuring script.
     Copyright (C) 2002-2005 Denis Sbragion
     
     This program may be freely redistributed under the terms of
     the GNU GPL and is provided to you as is, without any warranty
     of any kind. Please read the file COPYING for details.
     
     Usage:
      measure bits rate startf endf lslen lssil indev outdev impfile
   [sweepfile]
     
      bits: measuring bits (16 or 24)
      rate: sample rate
      startf: sweep start frequency in Hz
      endf: sweep end frequency in Hz
      lslen: log sweep length in seconds
      lssil: log sweep silence length in seconds
      indev: ALSA input device
      outdev: ALSA output device
      impfile: impulse response output file
      sweepfile: optional wav file name for the recorded sweep
     
     example: measure 16 44100 5 21000 45 2 plughw plughw impulse.pcm
   >>
    
   This script assumes that the measuring channel is on the left channel
and that the reference channel is the right one. To use it just take a
look at the sample command line provided above. You have to provide
proper ALSA input and output devices, but "plughw" usually works with
most soundcards.
  Using 24 bits of resolution to measure an impulse response is usually
just a waste of resources. In most rooms getting a recorded sweep with
more than 60 dB of S/N ratio is close to impossible, so 16 bits of
resolution are already plain overkill. On the other hand, thanks to the
strong noise rejection provided by the log sweep method, a sweep S/N
ratio of 60 dB is already high enough to get more than 90 dB of S/N
ratio in the recovered impulse response, at least with a 45 s sweep
running at a 44.1 KHz sample rate.
  The impulse response is what DRC works on, so it is the impulse
response that needs an high S/N ratio, not the sweep. If you really want
a better impulse response S/N ratio, or if you measure in a noisy
environment, increase the sweep length instead of using 24 bits of
resolution. A longer sweep will improve the S/N ratio of the impulse
response, increasing the resolution instead will provide no benefit at
all.
  Chris Birkinshaw created a modified version of the measure script
which adds Jack support. The script is named "measurejack" and you can
find it under the "source/contrib/MeasureJack" directory of the standard
distribution. For informations about Jack take a look at:
    http://jackit.sourceforge.net/ 
   Finally Ed Wildgoose created a simple program with about the same
functionality of the measure script. It works also under Windows and
being written in C, instead of being a simple shell script, it is less
dependent on other tools and usually provides a more reliable
functionality. You can download it from:
    http://www.duffroomcorrection.com/wiki/Simple_Automated_IR_Measuring
   _Tool 
  
  

4.4.4  Beware cheap, resampling, soundcards
-------------------------------------------
  
  Most cheap game oriented soundcards often include a sample rate
converter in their design, so that input streams running at different
sample rates can be played together by resampling them at the maximum
sample rate supported by the soundcard DAC. Usually this is 48 KHz as
defined by the AC97 standard. These sample rate converters often are of
abysmal quality, causing all sort of aliasing artifacts.
  Most deconvolution based impulse response measurement methods,
including the log sweep method, are quite robust and noise insensitive,
but cause all sorts of artifacts when non harmonic but signal related
distortion is introduced, even at quite low levels. The aliasing
artifacts introduced by low quality sample rate converters are exactly
of this kind and are one of the most common cause of poor quality
impulse response measurements and consequently of correction artifacts.
  

4.4.5  How to work around your cheap, resampling, soundcard
-----------------------------------------------------------
  
  Despite this, most of the times good measurements are possible even
out of cheap soundcards if the maximum sample rate supported by the DAC
is used, usually 48 KHz, so that the soundcard internal sample rate
converter isn't used at all. You can change the impulse response sample
rate after the measurement using high quality software sample rate
conversion algorithms (see section 4.5), thus preserving the impulse
response quality.
  To check the quality of the impulse response measurement perform a
loopback measurement, without using a reference channel else any
measurement problem will be washed out by the reference channel
compensation. The impulse response you get must be a single clean spike
much similar to that of a CD Player (see for example the upper graph of
picture 88, labeled "Dirac delta"). A bit of ringing before and/or after
the main spike is normal, but anything else is just an artifact. Only
when you are sure that the measurement chain is working as expected open
the loopback and do the real measurement, eventually adding also a
reference channel to compensate for any remaining soundcard anomaly.
  

4.5  Sample rate conversion
===========================
   
  If you have the impulse response sampled at a different rate than the 
one needed for the final filter, you need to convert the sample rate 
before creating or applying the filters. For example you might have a 48
 KHz impulse response but you may need to filter standard CD output at 
44.1 KHz. In this situation you can either convert the impulse response 
to 44.1 KHz before feeding it to DRC or you can convert the resulting 
filters to 44.1 KHz after DRC has created them. I generally prefer the 
first procedure, which leads to exact filter lengths in the DRC final 
windowing stage, but in both cases you need a good quality sample rate 
converter, which uses, for example, band limited interpolation. A
reasonable  choice, free both under Linux and Win32, is SoX, which may
be downloaded  at: 
    http://sox.sourceforge.net/ 
   Recent versions of SoX include some top quality sample rate
conversion routines. SoX also provides a lot of other features for sound
files manipulation. For a reference on band limited interpolation take a
look at:
    http://ccrma-www.stanford.edu/~jos/resample/ 
   Another free good sample rate converter comes from the shibatch audio
 tools suite. This sample rate converter provides a quality which is 
adequate for the task of converting the impulse response file before 
feeding it to DRC. You can find the shibatch audio tools at it at: 
    http://shibatch.sourceforge.net/ 
  
  

4.6  Correction tuning
======================
   
  Proper tuning of the correction filter generation procedure easily
provides a substantial improvement over the standard sample
configuration files provided along with DRC (see section 5.2). To
properly tune the filters to closely match your room behaviour there are
many different issues that should be taken into account.
  

4.6.1  Preventing pre-echo artifacts
------------------------------------
   
  One of the main problems in digital room correction are pre-echo
artifacts that arise when compensation accuracy is pushed above a
certain threshold. This pre-echo artifacts usually occur on narrow bands
and are easily audible as a sort of ringing or garble before transients
or sharp attacks. In order to avoid them there are basicly two options:
  
 
 
   - Reduce the correction on critical frequency regions where pre-echo 
   artifacts may arise. 
 
   - Use a minimum phase approach to avoid pre-echoes. This way you get
   increased ringing after the main spike instead of pre-echo, but this
   is usually masked both by our ear temporal masking and by the
   reverberant nature of common listening rooms, so it is much less
   audible, if audible at all.
   DRC uses both options in different steps of the correction procedure.
So in order to avoid pre-echo artifacts you basically have to:
  
  
   - Reduce the amount of correction applied to the excess phase 
   component by reducing the size of the frequency dependent window 
   applied. With the standard configuration files this is usually 
   everything that need to be done, because all the other procedures are
    already configured to avoid pre-echo problems. 
 
   - Use a long enough FFT where circular convolution is involved
   (basicly homomorphic deconvolution and pre-echo truncation
   inversion), because circular artifacts may easily become pre-echo.
 
   - Use the single side sliding lowpass prefiltering procedure; this is
   just because of small numerical errors in band windowing that causes
   small amounts of pre-echo on band edges.
 
   - Use the minimum phase versions for some of the accompanying
   procedures (peak and dip limiting for example)
 
   - Use the pre-echo truncation fast deconvolution for the inversion 
   procedure, with appropriate pre-echo truncation parameters. By the
   way,  if the excess phase component windowing parameters are already
   set  appropriately, this should not be needed. 
   The sample configuration files supplied are a good example of all
these options combined together. In normal situations you can use them
as they are changing only EPLowerWindow, EPWindowExponent, MPLowerWindow
and MPWindowExponent to fit your needs.
  

4.6.2  Preventing clipping
--------------------------
   
  One of the problems of real time correction is the prevention of DAC 
clipping caused by the filter intrinsic amplification. First of all the 
normalization factor to be used (see sections 6.12.9 and  6.2.10)
depends on the convolver used. Some convolvers want  the filter
normalized to the 16 bit range, i.e. 32768, most others want  a standard
normalization, i.e. normalization to +/- 1.0. For example  BruteFIR
needs a filter normalized to 1.0 to get 0 dB amplification  between
input and output. 
  All the normalization steps used within DRC, included those needed to
output the final filter (see sections 6.12.10 and 6.2.11), accept four
types of normalization: 	 
  	
   - S, i.e. sum normalization, also called L_1 norm 	
   - E, i.e. euclidean normalization, also called L_2 norm 	
   - M, i.e. Max normalization, also called L_oo norm 	
   - P, i.e. Peak normalization, i.e. normalization to the highest
   amplitude response peak 
   For a detailed description of the four types of normalization see
section 6.1.11.
  The S normalization guarantees against overflows in the output stream,
 i.e. it guarantees that if any input sample is never greater than X
than  any output sample is never greater than X multiplied by the 
normalization factor. This means also that if the normalization factor 
is 1 and the input sample is never greater than 32767 (i.e. the input is
 a 16 bit stream) the output is never greater than 32767, i.e. a 16 bit 
DAC on output will never clip or overflow. 
  Anyway, using common musical signals, and depending on the filter 
frequency response, the use of the S normalization might lead to filters
 with a global gain substantially lower than 1 (0 dB), i.e. filters with
 a typical output level which is lower, most of the times much lower, 
than the input level. With such low levels part of the resolution of the
 DAC gets lost. With normal musical signals it is usually safe to use a 
filter with an S normalization factor greater than 1, because, 
considering the typical frequency response of a room, and the 
corresponding reversed frequency response of the filter, overflows would
 occur in frequency ranges where typically there is not enough musical 
signal to cause it. 
  A good extimation of an adequate normalization factor might be
provided  by the P normalization, which rescales the filter so that the
highest  peak in the magnitude response corresponds to a 0 dB gain.
Contrary to  intuition this doesn't completely ensure that there would
never be  clipping on output, but for most common musical signals it
usually  provide a safe extimation without introducing excessive
attenuation.
  If you use BruteFIR one possible approach is to use 1 for the 
PSNormFactor and S for PSNormType and then use the rescaling and 
monitoring features of BruteFIR to boost the gain up to few dB below 
overflow with typical musical signal. You might try using a 0 dB white 
noise source as a sort of worst case situation. 
  Be careful setting the basic filter gain. I found that many recent 
musical recordings, especially compressed and rescaled pop music 
productions, cause output levels that are just 1 or 2 dB below the white
 noise worst case scenario. The degradation in the sound quality caused 
by DAC clipping is typically much more audible than the degradation you 
get loosing a single bit or less of your DAC resolution, especially if 
you use 16 bit DACs along with dithering or 24 bits DACs. 
  If you're unable to perform a test using 0 dB white noise as the input
 signal and for some reason you don't want to rely on the estimation 
performed by the P normalization, a simple rule of thumb is to use the E
 normalization with a normalization factor which is a couple of dB lower
 than the maximum gain allowed during peak limiting. With the standard 
configuration files, where the maximum allowed gain is never greater 
than about 6 dB, this means using a normalization factor around 0.3 - 
0.4 with convolvers which use 1.0 as the 0 dB reference level like 
BruteFIR, or using something like 10000 - 13000 with convolvers which 
use 32768 as the 0 dB reference level. 
  The default configuration files all use the E normalization with a 
normalization factor set to 1, leaving the task of scaling the filter
gain to avoid clipping to the convolver. With the default configuration
files you should set the convolver gain to something below -6 dB, which
is the default maximum gain allowed by the peak limiting procedure.
  

4.6.3  Some notes about loudspeaker placement
---------------------------------------------
  
  As most audio practitioneers already know, in a basic stereo
loudspeaker  configuration it is important that the distance between the
loudspeakers  and the listening position is exactly the same for both
loudspeakers,  and also not too different from the distance between the
two  loudspeakers themselves (the classical equilateral triangle
placement).  If this rule isn't satisfied usually the stereo image
become distorted  and confused. With digital room correction enabled
this rule becomes of  paramount importance. 
  DRC doesn't automatically compensate for delays caused by loudspeaker 
misplacement and having the two channels with near to perfect direct 
sound, both in phase and magnitude, makes any difference in the arrival 
time immediately and clearly audible, with a nasty phasey sound and a 
blurred stereo image. Less than 10 cm are enough to cause clearly 
audible problems, so take your time to measure the distance from both 
loudspeakers and the listening position before doing any measure, and 
also do your measures by placing the microphone exactly at the listening
 position. 
  Furthermore, with digital room correction it is worth to experiment
with  unusual speaker placements. Reflections from nearby walls are more
 difficult to correct when they are away from the main spike, so placing
 the speakers near to the walls, or may be even in the corners, might 
sometime give better results with DRC, provided that you place some 
absorbing material near the speakers to remove early reflections in the 
high frequency range, where DRC is able to correct only the direct 
sound. 
  This type of placement is exactly the opposite of what is usually done
if you don't use digital room correction, where it is usually better to
try to put loudspeakers away from the walls to avoid early reflections,
that cause major problems to the sound reproduction and almost always
boomy bass. Anyway, remember that there is no ready to use recipe to
find the best speaker placement, even with DRC in use, so a bit of
experimenting is always needed.
  

4.6.4  Some notes about channel balance
---------------------------------------
  
  DRC doesn't compensate for channel level imbalance, so this should be
done manually after correction by changing a little the filters level
until a perfect balance is achieved. This is of course better achieved
using an SPL meter with pink noise and proper weighting. Anyway after
correction the two channels start having a frequency response that is
pretty much the same, so achieving perfect balance becomes pretty easy
even by ear. Just use a mono male, or, better, female voice, and adjust
the filters level until the voice comes exactly from the center of both
loudspeakers.
  To achieve a good balance you might also use the level hints provided
by  DRC at the end of the correction procedure, provided that the
measured  impulse responses have levels that are directly related to the
original  levels of the channels, i.e. these levels haven't been changed
by the  measuring procedure itself.
  

4.6.5  Interchannel time alignment
----------------------------------
   
  First of all the current DRC release is able to compensate for
interchannel misalignment of only few samples, no more than  +/- 8  with
the default configuration files. Furthermore accurate time aligned
measurements must be supplied, using either the glsweep and lsconv tools
with a reference channel or some other tool providing the same degree of
accuracy.
  To get this limited time alignment you have to execute the following
steps:
  
 
 
   1. Execute DRC on one channel as usual. At the beginning of the DRC
   output on screen you will see a line like this one:
       
      <<Impulse center found at sample 1367280.
      >>
  Take note of the impulse center value. 
 
   2. After DRC has finished prepare the configuration files for the
   other channels as usual but change the BCImpulseCenterMode parameter
   to M and the BCImpulseCenter parameter from 0 to the value of the
   impulse center noted before for the first channel. This way DRC will
   use the value of the impulse center of the first channel as a
   reference for the other channels and will compensate for any
   misalignment with respect to the first channel. If channels are
   misaligned more than few samples this will cause errors in the
   correction filters, usually causing a rising frequency response, and
   so a bright sound.
  
  

4.6.6  How to tune the filters for your audio system
----------------------------------------------------
   
  A proper tuning of the filters for your audio system and your
listening room easily provides a substantial improvement over the
standard configuration files. The best way to do this is to use the
correction simulation provided by DRC and to check the results using the
Octave scripts supplied with the documentation (see section A), but if
you have little experience with measurements interpretation you can also
try to tune the correction by simple listening to the results, even
though it isn't an easy task.
  One of the most common mistakes performed in the tuning procedure is
the use of an excessive correction, which initially gives the impression
of a good result, but cause also the appearance of subtle correction
artifacts that becomes audible only with some specific musical tracks.
These artifacts often have a peculiar resonant behaviour so they become
audible only when they get excited by specific signals. To learn how to
recognize them try using the "insane.drc" sample configuration file,
which applies an overly excessive amount of correction, causing clearly
audible artifacts on all but the most damped rooms.
  The best procedure to use is to start from the minimal amount of
correction, like that provided by the minimal.drc or erb.drc correction
settings. If your impulse response measurements are of good quality
these minimalistic correction settings should already provide a
substantial improvement over the uncorrected system, without any
perceivable artifact. If this doesn't happen it's better to first double
check the measurements performed before fiddling with the correction
parameters. Remember that measurements problems are the most common
cause of unsatisfactory correction results.
  After this first test you can slowly switch to stronger correction
settings using the soft.drc, normal.drc, strong.drc and extreme.drc
settings, always listening to the results after each step, if possible
using quick switching between the filters. When correction artifacts
start to arise, which usually happens between the normal.drc settings
and the extreme.drc settings, it's time to stop and to start playing
with some specific correction parameters.
  The first parameters to modify are those that define the windowing
correction curve applied to the signal, i.e MPWindowExponent,
EPWindowExponent, RTWindowExponent, slowly reducing them to 0.95, 0.9,
0.85 and so on, down to about 0.7, thus reducing the correction in the
critical mid and mid-bass range. These are really sensitive parameters,
so changing them by as little as 0.01 easily cause an audible
difference, especially when you are close to the boundary where
correction artifacts start to appear. When the artifacts disappear you
can start increasing the windows applied to the bass range, slowly
increasing, by about a 5% at a time, the MPLowerWindow, EPLowerWindow,
RTLowerWindow parameters, until artifacts start to appear again. After
that you can decrease again the window exponent parameters until
artifacts disappear again, and so on.
  This procedure may be repeated until there's no further improvement or
 the parameters reach an excessive value, i.e below about 0.6 for the 
window exponents, above 1 second for the minimum phase and ringing 
truncation windowing parameters (MPLowerWindow, RTLowerWindow) and above
 100 ms for the excess phase windowing parameter (EPLowerWindow). 
Remember also to set the pre-echo truncation parameters
(ISPELowerWindow,  ISPEUpperWindow) according to the excess phase
windowing parameters (see  sections 6.8.4 and 6.8.5). 
  Of course the tuning procedure has to be carefully adapted to your
specific room, so, after a good tuning has been reached following the
basic procedure, you can further try playing a little with the available
parameters, applying even different values to each of them, proceeding
one at a time to avoid confusion. By the way, be careful, because after
the initial tuning the differences between the filters will start to be
quite subtle, most of the times will be barely audible, and quick
switching between the filters, possibly even under blind conditions,
will become almost mandatory to really understand what's happening and
which filter is better or at least audibly different.
  

5  Program compilation and execution
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=

  
  DRC can be compiled either under Win32 or Linux, but because of its
simplicity it will probably work under most operating systems with a
decent C++ compiler with support for the standard template library
(STL). The Win32 executable (drc.exe) is provided precompiled with the
standard DRC distribution under the sample directory, where there are
also the executables for the impulse response measuring tools
(glsweep.exe and lsconv.exe).
  A Makefile is provided for Linux and other Unixes, but it has been 
tested only under Fedora Core 11. To build the program under Linux 
usually what you have to do is just type "make" in the source  directory
of DRC, where the makefile resides. A Code::Blocks workspace  is also
available for use both under Win32 and Linux. Code::Blocks can  be
downloaded at:  	 
    http://www.codeblocks.org/ 
   The file drc.h contains a configurable define (UseDouble) which can
be set to use double or float as the data type used for all internal
computations. Despite some microscopic differences in the final output,
I have never found any real advantage using doubles as the internal
basic type.
  During the testing for the 3.1.0 release I have performed some tests
to check the signal to noise ratio of the output filters. Despite the
amount of processing performed and the fact that little effort has been
placed into keeping the maximum accuracy throughout the processing, even
using single precision arithmetic the signal to noise ratio of the final
filter resulted to be greater than 140 dB in the worst case. This is
more than 20 dB better than the signal to noise ratio provided by the
best DACs available in the world.
  Considering these results the supplied Win32 executable is compiled
for single precision. If you want to switch to the double precision you
have to recompile it yourself. Of course using the double data type
makes DRC a bit slower and, most important, much more memory intensive.
  Starting from version 2.4.0 DRC is able to use the Takuya Ooura and
GNU Scientific Library FFT routines, which are included in the
distributed package. The inclusion of these routines is controlled by
the UseGSLFft and UseOouraFft defines in drc.h. These routines are about
10 times faster than the standard routines used by DRC, but to use them
with the STL complex data type a clumsy hack has been used, and it is
not guaranteed that this hack will work with all the STL implementations
available. If it causes any problem simply comment out the UseGSLFft and
UseOouraFft defines in drc.h and recompile the program. This will force
DRC to use the older, slower but STL compliant FFT routines.
  The accuracy of the different FFT routines is pretty much the same.
The Ooura routines work only with powers of two lengths, so they are
used only with power of two lengths computations. Ooura FFT routines are
somewhat faster than the GSL routines but are also a little bit less
accurate. The default configuration uses only the GSL FFT routines,
providing the best compromise between speed and accuracy. The Ooura FFT
routines become useful when DRC is compiled for double precision
arithmetic.
  Most text files supplied with the standard distribution use Unix line
termination (LF instead of CR/LF). Be aware of this when opening files
under Win32 systems. WordPad is able to open LF terminated text files,
NotePad isn't.
  Finally an important note, especially for Win32 users. DRC is a
console program, it has no graphical interface. All program execution
parameters must reside in a plain ASCII text file which is supplied as
an argument on the program command line. In order to execute the program
you have to open a command prompt (or DOS Prompt or whatever is named a
console in your version of Windows) and type something like:
    
   <<drc test.drc
   >>
   followed by a carriage return (enter or return key). Test.drc should
be the text file already prepared with all the parameters needed to run
DRC.
  Under Linux of course you have to use a console program (the Linux
console, a terminal emulator like XTerm or something like this if you
are using XWindows). The DRC executable must be in the system path or in
the directory where you execute.
  

5.1  Command line parameters replacing
======================================
  
  Starting from version 2.6.2 all the parameters available in the
configuration file may be replaced by an equivalent parameter on the
command line. For example if you want just to change the input and
output filter files of the normal.drc sample configuration file you may
use a command like this: 	 
    
   <<drc --BCInFile=myfile.pcm --PSOutFile=myfilter.pcm normal.drc
   >>
   The parameter parsing procedure supports also quoting of filenames
with spaces and setting of strings to empty values, which is the same as
commenting a parameter in the configuration file. For example to use
some filename with spaces, to disable the output of the test convolution
file, to change the maximum allowed gain, all in a custom configuration
file with spaces in its name, you could use a command line like this:
    
   <<drc --BCInFile="my file.pcm" --PSOutFile="my filter.pcm" 
       --TCOutFile="" --PLMaxGain=3.5 "my custom config.drc"
   >>
  	 Along with all the default configuration parameters there is also a
special "--help" parameter that show the full list of all the available
parameters with the associated parameter type. The list of the
parameters is really long, so some pager is needed to see them all.
  

5.2  Sample configuration files
===============================
   
  DRC has started as an experimental program and because of this it has
a  lot of tunable parameters, actually more than 150. Only few of them
are  really important for the final filter correction quality. Most of
them  are used just to take a look at intermediate results and check
that  everything is working as expected. DRC flexibility might of course
be  used also to deal with complex or unusual situations or to
experiment  with weird configurations.
  Along with the DRC distribution six main sample configuration files
are  provided: minimal-XX.X.drc, soft-XX.X.drc, normal-XX.X.drc, 
strong-XX.X.drc, extreme-XX.X.drc, insane-XX.X.drc. The "XX.X' in the 
file name stands for the sample rate in KHz which the file is configured
 for. For example "normal-44.1.drc" is the normal configuration file 
for the 44.1 KHz sample rate. Considering that the only difference 
between the files is the base sample rate they are configured for, in 
the rest of this document all files are named omitting the sample rate 
part.
  The sample configuration files provide most parameters set to
reasonable  defaults, with stronger correction, but also worse listening
position  sensitivity, going from the minimal.drc settings to the
extreme.drc  settings. In the same directory of the configuration file
there is also  a sample impulse response (rs.pcm, this is the impulse
response of the  right channel of my previous HiFi system, in 32 bit
IEEE raw format) usable  with the sample configuration files to see just
what happens when DRC is  run.
  The insane correction settings are not meant for normal use but are
used just to provide an example of excessive correction that is going
for sure to cause audible correction artifacts. Using these settings
file you can easily check how correction artifacts actually sound like,
thus learning to identify them within normal filters while you are
tuning them for your audio system (see section 4.6.6).
  Another interesting sample configuration is the one provided by  the
"erb.drc" file. This file provides an accurate approximation of  the ERB
psychoacoustic scale (see figure 8). It  is important to notice that
basicly the correction isn't much stronger  than the "minimal.drc"
sample configuration, but being approximately  tuned to our ear
psychoacoustic resolution it is probably going to  provide a good
perceived correction accuracy with minimal listening  position
sensitivity, and so it is well suited for multiple listeners situations,
like home theater applications. 
  Starting form version 2.7.0 all sample configuration files are
available  for 44.1 KHz, 48 KHz, 88.2 KHz, 96 KHz sample rates. By the
way you  should be careful with sample rates above 44.1 KHz because most
of this  sample files have been simply derived from the 44.1 KHz version
without  testing them in real life situations. The sample configuration
files for  the higher sample rates aren't in the sample directory. To
avoid placing  a lot of similar files in the same directory the files
for the higher  sample rates are placed in the "src/config" directory.
  Remember also that all the sample correction files output the
correction  filter (rps.pcm) in 32 bit floating point format normalized
to 1.0,  which is the format suited for use with BruteFIR. Most sound
editors  expect 16 bits integer files normalized to 32768, so the file
above  might look either empty or completely clipped when opened with a
sound  editor without using the appropriate options. 
  

5.2.1  Target magnitude response
--------------------------------
   
  Starting from version 3.0.0 the basic target magnitude response is 
automatically generated by DRC using a specific procedure based on some 
documented psychoacoustic assumptions. See section  4.3 for the details.
Because of this  there should be no need to define a specific target
curve and a flat  target, with just some limiting for subsonic and
ultrasonic frequencies,  should be used instead. This is accomplished by
using the pa-XX.X.txt  target, which is now the default for all standard
configuration files  and is just a variation of the previous flat target
adjusted to better  work with the "B Spline" target transfer function
interpolation  procedure. The old target responses are retained for
those situations  where the old approach may be preferable, and may be
found under the  "source/target" directory. Of course the postfiltering
stage might be  used to adjust the magnitude response to taste, but for
a neutral  reproduction the target magnitude response should be left to
the flat  one. 
        --------------------------------------------------------
   
          [width=0.9@percent,keepaspectratio]figures/DBP-DTFCmp 
  Figure 10:  Comparison of the main target functions provided along
with DRC. 
                                     
   
        --------------------------------------------------------
  
  The most important postfiltering target magnitude response files 
supplied in the standard distribution (see section 6.12.7 
"PSPointsFile" for details) are subultra-XX.X.txt, bk-XX.X.txt, 
bk-2-XX.X.txt, bk-3-XX.X.txt (see figure 10).  Here again "XX.X" stands
for the sample rate used and is omitted in  the rest of this document.
The target response files for the higher  sample rates are available in
the "src/target" directory. 
  The first target response file provides just simple removal of 
overcompensation on the extremes of the frequency range and has a linear
 target frequency response, so it hasn't been plotted in figure  10. The
bk.txt file follows the Bruel & Kjaer  (i.e. Moeller) recommendations
for listening room frequency  response, i.e. linear from 20 Hz to 400
Hz, followed by a slow decrease  of 1 dB per octave up to 20 KHz. The
bk-2.txt file is similar to bk.txt  but it is linear up to 200 Hz and
then provides a slow tilt of 0.5 dB  per octave up to 20 KHz. The
bk-3.txt file is somewhat between bk-2.txt  and bk.txt, with a 0.5 dB
per octave tilt above 100 Hz. The versions  with the "sub" suffix are
the same target functions with the addition  of a steep subsonic filter.
The versions with the "spline" suffix are  again the same target
transfer functions but with a set of control  points suitable for the "B
Spline" target transfer function  interpolation. Figure 10 also show an
example  of PCHIP interpolation of the "bk-3-sub" target function. In
the sample  directory there are also some other simple postfiltering
target files. 
  Like the sample configuration files starting from version 2.7.0 the 
sample target responses are available for 44.1 KHz, 48 KHz, 88.2 KHz and
 96 KHz sample rates and they must be used with the corresponding set of
 configuration files. By the way the target response files for higher 
sample rates are simply extended versions of the 44.1 KHz target 
responses created by simply moving the last frequency point up to the 
Nyquist frequency. This means that for most configuration files there is
 either a gentle roll-off at higher frequency or a supersonic brickwall 
filter applied above 20 KHz. If you want to properly correct content 
above 20 KHz, provided that you have a microphone capable of recording 
ultrasonic frequencies, you have to adapt the supplied files to your 
needs. 
  

6  DRC Configuration file reference
*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*

  
  The DRC configuration file is a simple ASCII file with parameters in
the form:
<<ParamName = value
>>
  Everything after a '#' and blank lines are considered comments and are
ignored. Each parameter has a two character prefix which defines the
step the parameter refers to. These prefixes are:
  
  
   - BC = Base Configuration 
   - MC = Microphone Compensation stage 
   - HD = Homomorphic Deconvolution 
   - MP = Minimum phase Prefiltering stage 
   - DL = Dip Limiting stage 
   - EP = Excess phase Prefiltering stage 
   - PC = Prefiltering Completion stage 
   - IS = Inversion Stage 
   - PT = Psychoacoustic Target 
   - PL = Peak Limiting 
   - RT = Ringing Truncation stage 
   - PS = Postfiltering Stage 
   - MS = Minimum phase filter generation Stage 
   - TC = Test Convolution stage 
   DRC does some checks to ensure that each parameter provided has a
value that makes sense, but it isn't bulletproof at all with respect to
this. Providing invalid or incorrect parameters values may cause it to
fail, or even to crash.
  Parameters which are important for the quality of the generated
filters are marked with (*). When it makes sense a reasonable value or
range of values is also provided, but the range supplied is always
referred to the 44.1 KHz sample rate.
  Many parameters have often a value which is a power of two. This is 
mainly for performance reasons. Many steps require one or more FFT 
computations, which are usually much faster with arrays whose length is 
a power of two. The default values supplied are defined for a 44.1 KHz 
sample rate. If a different sample rate is used the supplied values 
should be scaled accordingly. 
  

6.1  BC - Base Configuration
============================
  
  

6.1.1  BCBaseDir
----------------
   
  This parameter define the base directory that is prepended to all file
parameters, like for example BCInFile, HDMPOutFile or PSPointsFile. This
parameter allow the implicit definition of a library directory where all
DRC support file might be placed.
  File parameters supplied on the command line are not affected by this
parameter unless the BCBaseDir parameter is also supplied on the command
line. File parameters supplied in the configuration file are instead
always affected by the BCBaseDir parameter, no matter if it has been
supplied in the configuration file or on the command line.
  

6.1.2  BCInFile
---------------
   
  Just the name of the input file with the input room impulse response.
  

6.1.3  BCInFileType
-------------------
   
  The type of the input file. D = Double, F = Float, I = Integer.
  

6.1.4  BCSampleRate
-------------------
   
  The sample rate of the input file. Usually 44100 or 48000.
  

6.1.5  BCImpulseCenterMode
--------------------------
   
  The impulse response impulse center may be set manually using the
BCImpulseCenter parameter or you may ask DRC to try to find it
automatically. If BCImpulseCenterMode is set to A DRC will look for the
impulse center within the input file. If BCImpulseCenterMode is set to M
DRC uses the impulse center supplied with the BCImpulseCenter parameter.
  Be careful when using automatic impulse center recognition. Strong
reflections or weird situations may easily fool the simple procedure
used by DRC, which simply looks for the sample with the maximum absolute
amplitude.
  

6.1.6  BCImpulseCenter (*)
--------------------------
   
  This is the position, in samples, of the time axis zero of the impulse
response read from BCInFile. Usually this is where the peak of the
impulse response is, but for complex situations it might not be easy to
identify where the zero is. Even few samples displacement in this
parameter may cause high frequency overcorrection, causing too bright
sound. If BCImpulseCenterMode is set to A this parameter is ignored.
  

6.1.7  BCInitWindow
-------------------
   
  Initial portion of the impulse response which is used to perform the 
correction. It should be long enough to accomodate for any subsequent 
windowing performed by DRC. The window is symmetrical with respect of 
the impulse center. If needed, the signal is padded with zeroes. Usual 
values are between 16384 and 131072, depending on the values of the 
parameters for the subsequent steps. This initial window may be further 
limited in subsequent steps, which sets the real window used.
  

6.1.8  BCPreWindowLen
---------------------
   
  This is the length of the window used to remove any noise coming
before the impulse center. This is usually just few samples, with a
typical value of 1024 samples, corresponding to 23.2 ms at a 44.1 KHz
sample rate. If this value is 0 this step is skipped
  

6.1.9  BCPreWindowGap
---------------------
   
  This is the central flat gap left in the previous windowing operation.
 Usually it is set to 0.75 * BCPreWindowLen, i.e. 768 samples with the 
standard BCPreWindowLen value. 
  

6.1.10  BCNormFactor
--------------------
   
  Initial normalization of the input impulse response. 0 means no
normalization, which is the default.
  

6.1.11  BCNormType
------------------
   
  Type of normalization applied. M means max normalization, i.e. the
input  signal is rescaled so that the maximum value of the samples is
equal to  the normalization factor. E means Euclidean normalization (L2
Norm),  i.e. the input signal is rescaled so that the RMS value of the
signal is  equal to the normalization factor. S means sum normalization
(L1 Norm),  i.e. the input signal is rescaled so that the sum of the
absolute values  of the samples is equal to the normalization factor. P
means peak  normalization i.e. the input signal is rescaled so that the
highest peak  in the signal magnitude response is equal to the
normalization factor. 
  

6.1.12  BCDLType, BCDLMinGain, BCDLStartFreq, BCDLEndFreq, BCDLStart, 
----------------------------------------------------------------------
BCDLMultExponent
----------------
   
  These parameters are used to set a mild dip limiting on the input
impulse  response. For a detailed description of these parameters see
the similar  procedure described in section 6.5. This stage is used 
just to prevent overflow or underflow problems in subsequent stages so 
under standard conditions there is no need at all to change these 
parameters. 
  

6.2  MC - Microphone Compensation
=================================
   
  Within this stage the microphone transfer function is invertend and 
applied to the input impulse response to compensate for any microphone 
aberration. If you want a microphone compensated filter you have to 
enable this stage. 
  The inversion is carried out by direct inversion of the values 
supplied in the microphone compensation file. So it is assumed that the
microphone response is easily invertible. This is usually true with any
decent microphone.
  

6.2.1  MCFilterType
-------------------
   
  This is the type of filter used for the microphone compensation stage 
stage. N means that the mic compensation stage is disabled, L means
linear phase filtering, M means minimum phase filtering.
  

6.2.2  MCInterpolationType
--------------------------
   
  This parameter is the same as the PSInterpolationType parameter (see
section 6.12.2) but applied to the mic compensation filter. The default
is H.
  

6.2.3  MCMultExponent
---------------------
   
  The multiplier exponent used for the homomorphic deconvolution used to
compute the minimum phase compensation filter. Usually a value of 2 or 3
is used.
  

6.2.4  MCFilterLen
------------------
   
  Length of the FIR filter used for microphone compensation. Usually
between 16384 and 65536.
  

6.2.5  MCNumPoints
------------------
   
  Number of points used for the definitions of the microphone frequency
response. If this parameter is 0 DRC automatically counts the number of
lines in the microphone frequency response file. See the following
parameters for details about the microphone frequency response
compensation.
  

6.2.6  MCPointsFile
-------------------
   
  This is the name of the file which contains the microphone frequency 
response to be compensated. The file format is identical to the one 
defined for the target frequency response (see section  6.12.7). Again
any phase specification get wiped out if  minimum phase filtering is
used. This usually isn't a problem because  most microphones suited for
measurement tasks are minimum phase systems,  so the minimum phase
compensation filter already has exactly the phase  response needed to
compensate for the microphone phase response. 
  In the sample directory there's a sample compensation file
(wm-61a.txt)  which is a generic compensation file for the Panasonic
WM-61A electrect  capsule. This file has been derived from average
values available on the  Internet, so don't expect to get perfect linear
frequency response using  it. There could be some difference among
different capsules of the same  type. In the same directory there's also
a compensation file for the  Behringer ECM8000 instrumentation
microphone. This is the measured  frequency response of a single unit,
i.e. it isn't even derived from an  average over many samples, so it may
be even less reliable than the  WM-61A compensation file. 
  

6.2.7  MCMagType
----------------
   
  This parameter selects how the amplitude of the target frequency
response is defined. L means linear amplitude (0.5 means half the level,
i.e about -6 dB), D means that the amplitude is expressed in dB.
  

6.2.8  MCFilterFile
-------------------
   
  This parameter set the file where the impulse response of the
microphone  compensation filter will be saved. This might be useful to
take a look  at the microphone compensation filter or to use it into
some other  program. By default it is disabled, i.e. commented out. 
  

6.2.9  MCOutWindow
------------------
   
  Final window after microphone compensation. Default value set to 0,
i.e. no windowing applied.
  

6.2.10  MCNormFactor
--------------------
   
  Normalization factor for the microphone compensated impulse response. 
Usually 0.0, i.e. disabled. 
  

6.2.11  MCNormType
------------------
   
  Normalization type for the microphone compensated impulse response. 
Usually E.
  

6.2.12  MCOutFile
-----------------
   
  Output file for the microphone compensated impulse response. Disabled,
 i.e. commented out, by default. The file generated by enabling this 
parameter might be used as input for the "createdrcplots" Octave  script
to generate the uncorrected response graph using a microphone 
compensated uncorrected response (see section A for  more details). 
  

6.2.13  MCOutFileType
---------------------
   
  Output file type for the microphone compensated impulse response. D = 
Double, F = Float, I = Integer. 
  

6.3  HD - Homomorphic Deconvolution
===================================
  
  

6.3.1  HDMultExponent
---------------------
   
  Exponent of the multiplier of the FFT size used to perform the
homomorphic deconvolution. The FFT size used is equal to the first power
of two greater than or equal to  BCInitWindow * (2 ^HDMultExponent).
Higher exponents give more accurate deconvolution, providing less
circular convolution artifacts. 
  With older DRC versions achieving low circular artifacts was not so
important because they were masked by the higher pre-echo artifacts in
other steps. Starting with version 2.0.0 it is possible to achieve
really low pre echo artifacts so circular artifacts now are an issue,
because when truncated by the pre-echo truncation inversion procedure
they may cause errors on the phase correction. In this situation a value
of at least 3 is suggested.
  

6.3.2  HDMPNormFactor
---------------------
   
  Normalization factor for the minimum phase component. Usually 1.
  

6.3.3  HDMPNormType
-------------------
   
  Normalization type for the minimum phase component. Usually E.
  

6.3.4  HDMPOutFile
------------------
   
  Output file for the minimum phase component. Usually not used
(commented out).
  

6.3.5  HDMPOutFileType
----------------------
   
  Output file type for the minimum phase component. D = Double, F =
Float, I = Integer.
  

6.3.6  HDEPNormFactor
---------------------
   
  Normalization factor for the excess phase component. Usually 1.
  

6.3.7  HDEPNormType
-------------------
   
  Normalization type for the excess phase component. Usually E.
  

6.3.8  HDEPOutFile
------------------
   
  Output file for the excess phase component. Usually not used
(commented out).
  

6.3.9  HDEPOutFileType
----------------------
   
  Output file type for the excess phase component. D = Double, F =
Float, I = Integer.
  

6.4  MP - Minimum phase Prefiltering
====================================
  
  

6.4.1  MPPrefilterType
----------------------
   
  This parameter can be either B for the usual band windowing
prefiltering  stage or S for the sliding lowpass method. The first
method splits the  input response into log spaced bands and window them
depending on some  parameters but basically with a window length which
decrease  exponentially with the center frequency of the band. The
sliding lowpass  method instead filters the impulse response with a time
varying lowpass  filter with a cutoff frequency which decreases
exponentially with the  sample position with respect to the time axis
zero. This last one is a  stepless procedure. 
  Using either a lowercase b or s for the MPPrefilterType parameters
enable the single side version of the prefiltering procedures. The
procedure is applied starting from the impulse center, leaving the first
half of the impulse response unchanged. This gives less pre-echo
artifacts, and should be used when the pre-echo truncation inversion
procedure is used. Please remember to set the prefiltering parameters to
values which are adequate for the procedure used.
  

6.4.2  MPPrefilterFctn
----------------------
   
  This parameter sets the type of prefiltering function used, i.e. P for
the usual inverse proportional function, or B for the bilinear transform
based prefiltering function. For a comparison between the two functions
see figure 6. The default is B.
  

6.4.3  MPWindowGap
------------------
   
  This parameter changes a little the window function (Blackman) used
for  the band windowing prefiltering stage. It sets a small flat unitary
gap,  whose length is expressed in samples, at the center of the window 
function, so that even if the impulse center is slightly misaligned with
 respect to the time axis zero there is no high frequency
overcorrection.  For band windowing prefiltering procedure usually this
overcorrection is  in the order of 0.1 - 0.2 dB at 20 KHz for errors of
2 to 3 samples,  so it is not important at all in real world situations,
but if you want  to fix even this small problem this parameter lets you
do it. 
  MPWindowGap should never be more than 2 sample less than MPUpperWindow
and it is usually no more than few samples (5 to 10). If in any
situation it is bigger than the calculated window DRC automatically
reduces the gap to 2 less than the applied window. When MPWindowGap is 0
DRC behaves exactly as in the older versions. For the sliding lowpass
procedure this sets just the window gap used for the initial windowing
before the procedure starts.
  

6.4.4  MPLowerWindow (*)
------------------------
   
  Length of the window for the minimum phase component prefiltering at
the bottom end of the frequency range. Longer windows cause DRC to try
to correct a longer part of the impulse response but cause greater
sensibility to the listening position. Typical values are between 16384
and 65536. MPLowerWindow must not be greater than BCInitWindow.
  

6.4.5  MPUpperWindow (*)
------------------------
   
  Length of the window for the minimum phase component prefiltering at
the upper end of the frequency range. Longer windows cause DRC to try to
correct a longer part of the impulse response but cause greater
sensibility on the listening position. Typical values are between 22 and
128. MPUpperWindow must be not greater than MPLowerWindow, and usually
is much shorter than that.
  

6.4.6  MPStartFreq
------------------
   
  Start frequency for the prefiltering stage. Usually 20 Hz or just
something less.
  

6.4.7  MPEndFreq
----------------
   
  End frequency for the prefiltering stage. Usually set at 20 KHz, i.e.
20000. Of course you must be using a sample rate which is greater than
40 KHz to set this above 20 KHz.
  

6.4.8  MPWindowExponent (*)
---------------------------
   
  This is the exponent used in the frequency dependent window length
computation for the band windowing procedure, or in the computation of
the time dependent cutoff frequency for the sliding lowpass procedure.
  The window length for band windowing is computed with the following
expression:
                                    1        
                              -------------- 
                          W =             WE 
                              A * (F + Q)    
   Where W is the window length, F is the normalized frequency, WE is
the window exponent, A and Q are computed so that W is equal to
MPLowerWindow at MPStartFreq and is equal to MPUpperWindow at MPEndFreq.
If you set MPLowerWindow equal to the value used for MPInitWindow in DRC
1.2, set MPWindowExponent to the same value of version 1.2 and set
MPUpperWindow to the value you got at the upper limit of the frequency
range in version 1.2 you should get results much similar to the 1.2 DRC
release.
  In a similar way the cutoff frequency for the sliding lowpass
prefiltering stage is computed with:
                                    1        
                              -------------- 
                          F =             WE 
                              A * (W + Q)    
   with identical parameters but reversed perspective, i.e. the cutoff
frequency is computed from the window length and not the other way
around. In both cases W and F are considered normalized between 0 and 1.
  These parametric functions are used when the proportional function is
selected using the MPPrefilterFctn (see section 6.4.2) parameter. The
parametric functions derived from the bilinear transformation are quite
different and more complicated, so they aren't explained here.
  Changing the window exponent provides different prefiltering curves,
see  section 4.2 for a deeper explanation.  Increasing the window
exponent gives higher correction in the midrange.  Typical values are
between 0.7 and 1.2. 
  

6.4.9  MPFilterLen
------------------
   
  Filter length, in taps, used to perform band splitting or sliding
lowpass prefiltering of the input signal. Higher values give better
filter resolution but require a longer computation. Typical values for
band windowing are between 4096 and 65536. Sometimes may be useful to
use short filters (64 - 512 taps) to get a more "fuzzy" correction at
lower frequencies.
  With the sliding lowpass procedure similar filters should be used.
Usually the filter length is in the 512 - 65536 range. Short filters (16
- 64 taps) gives a similar fuzzy correction at the bottom end, but with
a different behaviour than band windowing.
  

6.4.10  MPFSharpness (*)
------------------------
   
  This parameter applies only to the sliding lowpass prefiltering
procedure and control the sharpness of the filtering performed in the
filtered region of the time-frequency plane. A value of 1.0 provides the
same behaviour of version 2.3.1 of DRC and provides the maximum
allowable filtering sharpness without affecting the direct sound, but
also creates a substantial amount of spectral spreading in the filter
transition region of the time-frequency plane. Values above 1.0 increase
the spectral spreading up to a point where it starts affecting also the
direct sound, with the introduction of some ripple in the direct sound
itself. Values below 1.0 reduce the spectral spreading in the filtered
region at the expense of a little reduction in the filter sharpness.
Typical values for this parameter are between 0.1 and 0.75, with a
default value of 0.25.
  

6.4.11  MPBandSplit
-------------------
   
  Fractional octave splitting of band windowing. Band windowing is
performed in  1 / MPBandSplit  of octave bands. Usual values are between
2 and 6. The higher this value the higher should be MPFilterLen. Values
greater than 6 usually give no improvements.
  For the sliding lowpass prefiltering this just gives the rate at which
log messages are reported during the prefiltering procedure and has no
effect on the prefiltering procedure itself, which is always stepless.
  

6.4.12  MPHDRecover
-------------------
   
  After prefiltering the minimum phase component may be no longer
minimum phase, with a bit of excess phase component added. Setting this
parameter to Y enable a second homomorphic deconvolution on the
prefiltered minimum phase component to make it minimum phase again. This
is important especially if the pre-echo truncation inversion procedure
is used. This procedure assumes that the minimum phase part really is
minimum phase, so skipping this step may cause it to fail in avoiding
pre-echo artifacts.
  

6.4.13  MPEPPreserve
--------------------
   
  Setting this to Y causes the excess phase part of the filtered impulse
response to be preserved after the MPHDRecover step. This excess phase
part is then convolved with the excess phase part of the filtered
impulse response to preserve it and invert it. This provides a slight
improvement in the direct sound phase response. The default value is Y.
  

6.4.14  MPHDMultExponent
------------------------
   
  Exponent of the multiplier of the FFT size used to perform the
homomorphic deconvolution described above. The FFT size used is equal to
the first power of two greater than or equal to  MPPFFinalWindow * (2
^MPHDMultExponent). Higher exponents give more accurate results, but
require a longer computation. Usually a value of 2 or 3 is used. If this
parameter is less than 0 no multiplier will be used. Be careful because
if the FFT size isn't a power of two the procedure can take a long time
to complete.
  

6.4.15  MPPFFinalWindow
-----------------------
   
  Final window of the prefiltering stage. Usually the same as
MPLowerWindow or just something more. If set to 0 no windowing is
applied.
  

6.4.16  MPPFNormFactor
----------------------
   
  Normalization factor for the minimum phase component after
prefiltering. Usually 0.
  

6.4.17  MPPFNormType
--------------------
   
  Normalization type for the minimum phase component after windowing.
Usually E.
  

6.4.18  MPPFOutFile
-------------------
   
  Output file for the minimum phase component after band windowing.
Usually not used (commented out).
  

6.4.19  MPPFOutFileType
-----------------------
   
  Output file type for the minimum phase component after windowing. D =
Double, F = Float, I = Integer.
  

6.5  DL - Dip Limiting
======================
   
  

6.5.1  DLType
-------------
   
  To prevent numerical instabilities during the inversion stage, deep
dips in the frequency response must be limited (truncated). This
parameter sets the type of dip limiting performed. L means linear phase,
i.e. it applies a linear phase filter that removes dips below a given
threshold, M means minimum phase, i.e. it uses a minimum phase filter to
achieve the same result. 
  Starting with version 2.0.0 DRC performs this step only on the
prefiltered minimum phase part, just before performing the second
homomorphic deconvolution, if enabled. So if the MPHDRecover parameter
is set to Y and the MPEPPreserve parameter is set to N there is almost
no difference between the two procedures, because the subsequent
homomorphic deconvolution stage wipes out any phase difference giving
just a minimum phase signal. Any difference would be caused just by
numerical errors.
  

6.5.2  DLMinGain
----------------
   
  This is the minimum gain allowed in the frequency response of the
prefiltered signal. Values lower than this will be truncated. Typical
values are between 0.1 and 0.5. These are absolute values with respect
to the RMS value, i.e. 0.1 is about -20 dB, 0.5 is about -6 dB.
  

6.5.3  DLStartFreq
------------------
   
  Start frequency where the reference RMS level used for dip limiting is
computed.
  

6.5.4  DLEndFreq
----------------
   
  End frequency where the reference RMS level used for dip limiting is
computed.
  

6.5.5  DLStart
--------------
   
  Setting this parameter to a value between 0.0 and 1.0 enables the
"soft clipping" dip limiting procedure. Everything below  DLStart *
DLMinGain , with respect to the RMS value, get rescaled so that it ends
up between  DLStart * DLMinGain  and DLMinGain. Values for this
parameter usually are between 0.5 and 0.95, with a typical value of
0.75. Setting this parameter to a value equal to or greater then 1.0
cause DRC to switch to hard clipping of the frequency response.
  

6.5.6  DLMultExponent
---------------------
   
  Exponent of the multiplier of the FFT size used to perform the dip 
limiting stage. The FFT size used is equal to the first power of two 
greater than or equal to  (MPBWFinalWindow + EPBWFinalWindow - 1) *  (2
^DLMultExponent) . Higher exponents give more accurate dip  limiting,
but requires a longer computation. Usually a value of 2 or 3  is used.
If this parameter is less than 0 no multiplier will be used. Be  careful
because if the FFT size isn't a power of two the procedure might take a
long time to complete. 
  

6.6  EP - Excess phase Prefiltering
===================================
  
  The excess phase prefiltering is performed pretty much the same way as
the minimum phase prefiltering, so the parameters are almost identical,
even though with different values.
  

6.6.1  EPPrefilterType
----------------------
   
  Same as MPPrefilterType but for the excess phase component.
  

6.6.2  EPPrefilterFctn
----------------------
   
  Same as MPPrefilterFctn but for the excess phase component.
  

6.6.3  EPWindowGap
------------------
   
  Same as MPWindowGap but for the excess phase component.
  

6.6.4  EPLowerWindow (*)
------------------------
   
  Same as MPLowerWindow but for the excess phase component. Typical
values are between 1024 and 4096. As a rule of thumb you can take: 	 
                  EPLowerWindow  =  MPLowerWindow / A 
   with A going from 16 to 32 and a typical value of 24.  EPLowerWindow
must be not greater than BCInitWindow. 
  

6.6.5  EPUpperWindow (*)
------------------------
   
  Same as MPUpperWindow but for the excess phase component. Typical
values are between 22 and 128. As a rule of thumb you can take:
                    	 EPUpperWindow = MPUpperWindow 
  
  

6.6.6  EPStartFreq
------------------
   
  Start frequency for the prefiltering stage. Usually 20 Hz or just
something less.
  

6.6.7  EPEndFreq
----------------
   
  End frequency for the prefiltering stage. Usually set at 20 KHz, i.e.
20000. Of course you must be using a sample rate which is greater than
40 KHz to set this above 20 KHz.
  

6.6.8  EPWindowExponent (*)
---------------------------
   
  Same as MPWindowExponent but for the excess phase component. See
discussion on MPWindowExponent. Usual values for this parameter are
between 0.5 and 1.2, depending on the value of EPInitWindow. As a rule
of thumb you can take: 	 
                  EPWindowExponent = MPWindowExponent 
  
  

6.6.9  EPFilterLen
------------------
   
  Filter length, in taps, used to perform band splitting of the input
signal or sliding lowpass prefiltering. Higher values gives better
filter resolution but require a longer computation. Typical values for
band windowing are between 4096 and 65536. Sometimes may be useful to
use short filters (64 - 512 taps) to get a more "fuzzy" correction at
lower frequencies.
  With the sliding lowpass procedure similar filters should be used.
Usually the filter length is in the 512 - 65536 range. Short filters (16
- 64 taps) gives a similar fuzzier correction at the bottom end, but
with a different behaviour than band windowing.
  This value is usually equal to MPFilterLen.
  

6.6.10  EPFSharpness (*)
------------------------
   
  Same as MPFSharpness but applied to the excess phase part.
  

6.6.11  EPBandSplit
-------------------
   
  Fractional octave splitting of band windowing. Band windowing is
performed in  1 / MPBandSplit  of octave bands. Usual values are between
2 and 6. The higher this value the higher should be MPFilterLen. Values
greater than 6 usually give no improvements.
  For the sliding lowpass prefiltering this just gives the rate at which
log messages are reported and has no effect on the prefiltering
procedure, which is always stepless.
  This value is usually equal to MPBandSplit.
  

6.6.12  EPPFFinalWindow
-----------------------
   
  Final window of the prefiltering stage. Usually the same as
EPInitWindow or just something more. If set to 0 no windowing is
applied.
  

6.6.13  EPPFFlatGain
--------------------
   
  After band windowing the excess phase component usually need
reequalization to get the flat frequency response it must have. This is
the gain applied with respect to the RMS level of the signal to get this
flat frequency response. Usually 1, a value of 0 disables this step.
Skipping this step, i.e. setting this parameter to 0, usually gives bad
results.
  

6.6.14  EPPFOGainFactor
-----------------------
   
  This parameter controls how the excess phase flattening set by the 
previous parameter is performed. Setting this to 0 tries to get a 
perfectly flat excess phase component, as in version 1.3.0 of DRC. This 
parameter has been introduced to balance between the need of a flat 
excess phase response and a perfect control of the direct sound, usually
 achieved without any flattening. Unfortunately so far the supposed 
balance always proved really difficult to find in any real world 
situation, so this parameter is always set to 0 in the standard 
configuration file. The procedure has been left just for experimental 
purposes if some unusual situation need to be handled. 
  Furthermore this parameter applies only to the linear phase and
minimum  phase excess phase flattening, it isn't available for the D
type of  excess phase flattening. 
  

6.6.15  EPPFFlatType
--------------------
   
  This is the type of procedure adopted for the excess phase component
renormalization. L means applying linear phase renormalization, M means
applying minimum phase renormalization, D means applying another
homomorphic deconvolution stage to extract just the excess phase
component of the prefiltered excess phase component. L applies a linear
phase filter that equalizes the excess phase amplitude response to flat,
M means minimum phase, i.e. it uses a minimum phase filter to achieve
the same result. The D procedure provides the same effect of the M
procedure when EPPFOGainFactor is equal to 0. Any difference is just
caused by numerical errors.
  

6.6.16  EPPFFGMultExponent
--------------------------
   
  Exponent of the multiplier of the FFT size used to perform the
frequency response flattening. The FFT size used is equal to the first
power of two greater than or equal to  EPBWFinalWindow * (2
^EPPFFGMultExponent) . Higher exponents give more accurate results, but
require a longer computation. This parameter should be set using the
same criteria described in HDMultExponent. If this parameter is less
than 0 no multiplier will be used. Be careful because if the FFT size
isn't a power of two the procedure might take a long time to complete.
  

6.6.17  EPPFNormFactor
----------------------
   
  Normalization factor for the excess phase component after band
windowing. Usually 0, i.e. disabled.
  

6.6.18  EPPFNormType
--------------------
   
  Normalization type for the excess phase component after windowing.
Usually E.
  

6.6.19  EPPFOutFile
-------------------
   
  Output file for the excess phase component after windowing. Usually
not used (commented out).
  

6.6.20  EPPFOutFileType
-----------------------
   
  Output file type for the excess phase component after windowing. D =
Double, F = Float, I = Integer.
  

6.7  PC - Prefilter Completion
==============================
  
  The prefilter completion stage combines the prefiltered minimum phase
and excess phase parts together again. The impulse response recovered
after prefilter completion defines the impulse response of the system as
seen by the correction applied by DRC.
  

6.7.1  PCOutWindow
------------------
   
  Final window after prefiltering completion stage and before impulse 
inversion. This is usually between 8192 and 65536. Values greater than 
65536 make no sense, giving a filter resolution lower than 1 Hz at a 
44.1 KHz sample rate. Furthermore inversion of signals longer than 65536
 samples may require a lot of time. Starting with version 2.0.0 this
step  is no longer needed with the pre-echo truncation fast
deconvolution  inversion method, which works directly on the minimum and
excess phase  components from the prefiltering stages. So if PCOutFile
is not defined  and ISType is set to T this step is completely skipped. 
  

6.7.2  PCNormFactor
-------------------
   
  Normalization factor for the prefiltered signal. Usually 0, i.e.
disabled.
  

6.7.3  PCNormType
-----------------
   
  Normalization type for the prefiltered signal. Usually E.
  

6.7.4  PCOutFile
----------------
   
  Output file for the prefiltered signal. Usually not used (commented
out).
  

6.7.5  PCOutFileType
--------------------
   
  Output file type for the prefiltered signal. D = Double, F = Float, I
= Integer.
  

6.8  IS - Inversion Stage
=========================
  
  

6.8.1  ISType
-------------
   
  Type of inversion stage. L uses the usual Toeplitz least square
inversion, T activates the pre-echo truncation fast deconvolution.
  

6.8.2  ISPETType
----------------
   
  This sets the type of pre echo truncation applied when ISType is T. f 
means a fixed pre-echo truncation, s means a time dependent pre-echo 
truncation applied using the usual single side sliding low-pass 
procedure, but with reversed behaviour, i.e. only what comes before the 
impulse center is processed. Starting with version 2.7.0 this is set to 
f and pre-echo truncation is basicly disabled because it is already 
carried out by the excess phase prefiltering procedure. 
  

6.8.3  ISPrefilterFctn
----------------------
   
  Same as MPPrefilterFctn but for the pre-echo truncation windowing. It
is  used only when ISPETType is set to s. 
  

6.8.4  ISPELowerWindow
----------------------
   
  When ISPETType is f this is the number of samples before the impulse 
center where the inverted impulse response is considered pre-echo. 
Starting with version 2.7.0 this is is usually set to half the value of 
EPLowerWindow so that the pre-echo truncation procedure provides just a 
mild windowing. When ISPETType is s this is the number of samples 
considered pre-echo at the ISPEStartFreq frequency, with a typical value
 equal to EPLowerWindow. 
  

6.8.5  ISPEUpperWindow
----------------------
   
  When ISPETType is f this is the number of samples before the impulse 
center where the pre-echo region, defined by the previous parameter, 
ends, and the full impulse response of the inverted filter should start.
 Starting with version 2.7.0 this is usually set to about 0.75 * 
ISPELowerWindow so that the pre-echo truncation procedure is limited to 
a mild windowing used only to avoid small steps in the impulse response 
attack caused by small numerical errors. When ISPETType is s this is the
 number of sample considered pre-echo at the ISPEEndFreq frequency, with
 a typical value equal to EPUpperWindow. 
  

6.8.6  ISPEStartFreq
--------------------
   
  Start frequency for the sliding low pass pre-echo truncation
procedure. Usually 20 Hz. Used only when ISPETType is s.
  

6.8.7  ISPEEndFreq
------------------
   
  End frequency for the sliding low pass pre-echo truncation procedure.
Usually 20000 Hz. Used only when ISPETType is s.
  

6.8.8  ISPEFilterLen
--------------------
   
  Length of the filter used for the pre-echo truncation sliding lowpass
procedure. Usually 8192. Used only when ISPETType is s.
  

6.8.9  ISPEFSharpness
---------------------
   
  Same as MPFSharpness, but applied to the inversion stage pre-echo 
truncation. Here slightly bigger values usually provide better results 
because of the shorter windowing. Used only when ISPETType is s. The 
default value is 0.5. 
  

6.8.10  ISPEBandSplit
---------------------
   
  For the sliding lowpass prefiltering this just gives the rate at which
log messages are reported and has no effect on the prefiltering
procedure, which is always stepless. Used only when ISPETType is s.
  

6.8.11  ISPEWindowExponent
--------------------------
   
  Window exponent applied to the pre-echo truncation sliding lowpass
procedure. Usual values goes from 0.5 to 1.5, with a typical value of
1.0. Used only when ISPETType is s.
  

6.8.12  ISPEOGainFactor
-----------------------
   
  This parameter has the same effect of the EPPFOGainFactor (see section
6.6.14) but applied to the renormalization of the excess phase part of
the inverse filter after pre-echo truncation. Used in conjunction with
the EPPFOGainFactor parameter, this parameter can be used to balance the
amount of correction applied to the direct sound compared to the amount
of correction applied to the reverberant field. A negative value
disables the renormalization. Default is 0.0.
  

6.8.13  ISSMPMultExponent
-------------------------
   
  This is the exponent of the multiplier for the S inversion stage,
using the longest of the input and output signals as a basis. This
parameter should be set using the same criterion used for the
MPHDMultExponent parameters and a values of at least 3 is suggested.
  

6.8.14  ISOutWindow
-------------------
   
  Final window after inversion stage. Usually 0, i.e. disabled, with the
L type inversion stage. With the S type this is the output filter size
and can be any length but usually is between 8192 and 65536. If it is 0
than a length equal to  MPPFFinalWindow + EPPFFinalWindow - 1 , i.e. the
length of the convolution of the two components together, is assumed and
no windowing is applied to the output filter.
  

6.8.15  ISNormFactor
--------------------
   
  Normalization factor for the inverted signal. Usually 0, i.e.
disabled.
  

6.8.16  ISNormType
------------------
   
  Normalization type for the inverted signal. Usually E.
  

6.8.17  ISOutFile
-----------------
   
  Output file for the inverted signal. Usually not used (commented out).
  

6.8.18  ISOutFileType
---------------------
   
  Output file type for the inverted signal. D = Double, F = Float, I =
Integer.
  

6.9  PT - Psychoacoustic Target
===============================
   
  This stage computes a psychoacoustic target response based on the 
magnitude response envelope. 
  

6.9.1  PTType
-------------
   
  Defines the type of psychoacoustic target filter to use. N means no 
filter, thus skipping the psychoacoustic target stage completely. M 
means that a minimum phase filter is used and L means that a linear 
phase filter is used. The default is M. 
  

6.9.2  PTReferenceWindow (*)
----------------------------
   
  This parameter define the size used to window the corrected impulse 
response. The windowed response is then used to compute the magnitude 
response envelope that the target response is based upon. Usually a 
portion of the impulse response going from 150 ms to 500 ms is used. The
 default value is 26460, corresponding to a symmetric window, 300 ms
long  on each side, at 44100 Hz sample rate. 
  

6.9.3  PTDLType, PTDLMinGain, PTDLStartFreq, PTDLEndFreq, PTDLStart, 
---------------------------------------------------------------------
PTDLMultExponent
----------------
   
  These parameters are used to set a small dip limiting on the corrected
 impulse response in order to avoid numerical problems in the inversion 
of the magnitude response envelope. For a detailed description of these 
parameters see the similar procedure described in section  6.5. This
stage is used just to prevent overflow or  underflow problems so under
standard conditions there is no need at all  to change these parameters.

  

6.9.4  PTBandWidth (*)
----------------------
   
  This parameter define the resolution used for the computation of the 
magnitude response envelope. It is defined as fraction of octaves, so a 
value of 0.25 means a resolution of 1/4 of octave. Values below 0 down 
to -1 causes the adoption of the Bark scale, values below -1 causes the 
adoption of the ERB scale. The default value is -2, which means that the
 computation is performed on the ERB scale. 
  

6.9.5  PTPeakDetectionStrength (*)
----------------------------------
   
  This parameter define how close the magnitude response envelope will
be  to to the peaks in the unsmoothed spectrum. Higher values provide a 
closer match. Typical values are between 5 and 30, with the default 
value, based on documented psychoacoustic assumptions, set to 15. Values
 above 50 are probably going to cause numerical problems and should be 
avoided. 
  

6.9.6  PTMultExponent
---------------------
   
  Multiplier exponent for the computation of the magnitude response 
envelope. Default is 0. 
  

6.9.7  PTFilterLen
------------------
   
  Length of the psychoacoustic target filter. Default set to 65536.
  

6.9.8  PTFilterFile
-------------------
   
  Output file for the psychoacoustic target filter. Usually not  used
(commented out).
  

6.9.9  PTFilterFileType
-----------------------
   
  Output file type for the psychoacoustic target filter. D = Double, F =
 Float, I = Integer.
  

6.9.10  PTNormFactor
--------------------
   
  Normalization factor for the inverted signal after convolution with
the psychoacoustic target filter. Usually 0, i.e. disabled.
  

6.9.11  PTNormType
------------------
   
  Normalization type for the inverted signal after convolution with the
psychoacoustic target filter. Usually E.
  

6.9.12  PTOutFile
-----------------
   
  Output file for the inverted signal after convolution with the 
psychoacoustic target filter. Usually not used (commented out). 
  

6.9.13  PTOutFileType
---------------------
   
  Output file type for the inverted signal after convolution with the 
psychoacoustic target filter. D = Double, F = Float, I = Integer. 
  

6.9.14  PTOutWindow
-------------------
   
  Normalization factor for the inverted signal after convolution with
the  psychoacoustic target filter. Usually 0, i.e. disabled.
  

6.10  PL - Peak Limiting
========================
  
  The peak limiting stage limits the maximum allowed gain of the filter
to prevent amplification and speaker overload.
  

6.10.1  PLType
--------------
   
  Type of peak limiting applied. L means linear phase, M means minimum
phase. If PSFilterType is set to T this should be set to M to ensure
that the initial zero valued part is preserved.
  

6.10.2  PLMaxGain
-----------------
   
  Maximum gain allowed in the correction filter. Peaks in the correction
filter amplitude response greater than this value will be compressed to
PLMaxGain. Typical values are between 1.2 and 4. These are absolute
values with respect to the RMS value, i.e. 1.2 is about 1.6 dB and 4 is
about 12 dB. This peak limiting stage is used to prevent speaker or
amplifier overloading, resulting in dynamic range limitations which are
subjectively worse than some narrow dip in the frequency response. A
typical value is 2.0, i.e. 6 dB.
  

6.10.3  PLStart
---------------
   
  Setting this parameter to a value between 0.0 and 1.0 enables the
"soft clipping" peak limiting procedure. Everything above  PLStart *
PLMaxGain , with respect to the RMS value, get rescaled so that it ends
up between  PLStart * PLMaxGain  and about PLMaxGain. Values for this
parameter usually are between 0.5 and 0.95, with a typical value of
0.75. Setting this parameter to a value equal to or greater than 1.0
switch to hard clipping of the magnitude response.
  

6.10.4  PLStartFreq
-------------------
   
  Start frequency where the reference RMS level used for peak limiting
is computed. Default value set to 20 Hz.
  

6.10.5  PLEndFreq
-----------------
   
  End frequency where the reference RMS level used for peak limiting is
computed. Default value set to 20000 Hz.
  

6.10.6  PLMultExponent
----------------------
   
  Exponent of the multiplier of the FFT size used to perform the peak
limiting stage. The FFT size used is equal to the first power of two
greater than or equal to  PSOutWindow * (2 ^PLMultExponent) . Higher
exponents give more accurate peak limiting, but requires a longer
computation. Usually a value of 2 or 3 is used. If this parameter is
less than 0 no multiplier will be used. Be careful because if the FFT
size isn't a power of two the procedure can take a long time to
complete.
  

6.10.7  PLOutWindow
-------------------
   
  Final window after peak limiting. Usually 0, i.e. disabled.
  

6.10.8  PLNormFactor
--------------------
   
  Normalization factor for the final filter. Usually 0, i.e. disabled. 
  

6.10.9  PLNormType
------------------
   
  Normalization type for the peak limited filter, usually E.
  

6.10.10  PLOutFile
------------------
   
  Output file for the peak limited filter. Usually disabled (commented
out).
  

6.10.11  PLOutFileType
----------------------
   
  Output file type for the final filter. D = Double, F = Float, I =
Integer.
  

6.11  RT - Ringing Truncation
=============================
   
  The ringing truncation stage applies a further frequency dependent
windowing to the correction filter. The truncation parameters are pretty
similar to those of the prefiltering stage and usually have also much
similar values.
  

6.11.1  RTType
--------------
   
  This parameter can be either B or b for the band windowing method, S
or s for the sliding lowpass method or N to disable the ringing
truncation stage. See section 4.2 and 6.4.1 for further details.
  

6.11.2  RTPrefilterFctn
-----------------------
   
  Same as MPPrefilterFctn but for the ringing truncation windowing.
  

6.11.3  RTWindowGap
-------------------
   
  This parameter changes a little the window function (Blackman) used
for the band windowing or the sliding lowpass windowing. See section
6.4.3 for further details.
  

6.11.4  RTLowerWindow (*)
-------------------------
   
  Length of the window at the bottom end of the frequency range. Usually
set to the same value of MPLowerWindow.
  

6.11.5  RTUpperWindow (*)
-------------------------
   
  Length of the window at the upper end of the frequency range. Usually
set to the same value of MPUpperWindow.
  

6.11.6  RTStartFreq
-------------------
   
  Start frequency for the windowing. Usually 20 Hz or just something
less.
  

6.11.7  RTEndFreq
-----------------
   
  End frequency for the windowing. Usually set to 20000.
  

6.11.8  RTWindowExponent (*)
----------------------------
   
  This is the exponent used in the frequency dependent window length
computation for the band windowing procedure, or in the computation of
the time dependent cutoff frequency for the sliding lowpass procedure.
See section 6.4.8 for further details. Usually set to the  same value of
MPWindowExponent.
  

6.11.9  RTFilterLen
-------------------
   
  Filter length, in taps, used to perform band splitting or sliding
lowpass prefiltering of the input signal. Usually the same as the one
used in the prefiltering stage.
  

6.11.10  RTFSharpness (*)
-------------------------
   
  This parameter applies only to the sliding lowpass prefiltering
procedure and control the sharpness of the filtering performed in the
filtered region of the time-frequency plane. See section 6.4.10 for
further details.
  

6.11.11  RTBandSplit
--------------------
   
  Fractional octave splitting of band windowing. See section 6.4.11 for
further details.
  

6.11.12  RTOutWindow
--------------------
   
  Final window of the stage. Usually set to 0, i.e. disabled.
  

6.11.13  RTNormFactor
---------------------
   
  Normalization factor for the minimum phase component after windowing.
Usually 0.
  

6.11.14  RTNormType
-------------------
   
  Normalization type for the minimum phase component after windowing.
Usually E.
  

6.11.15  RTOutFile
------------------
   
  Output file for the filter after windowing. Usually not used
(commented out).
  

6.11.16  RTOutFileType
----------------------
   
  Output file type for the filter after windowing. D = Double, F =
Float, I = Integer.
  

6.12  PS - Postfiltering Stage
==============================
   
  During the postfiltering stage the final target transfer function is
applied to the filter and the filter is normalized to suitable values
for the convolver used.
  

6.12.1  PSFilterType
--------------------
   
  This is the type of filter used for the postfiltering stage. L means
the usual linear phase filtering, M means minimum phase filtering, T
means minimum phase filtering with initial zero truncation. If the
pre-echo truncation inversion is used and the final post filtering stage
is minimum phase all the filter taps before ISPELowerWindow are zero
(there could be some roundoff errors that make them different from zero,
but considering them zero makes no difference for our needs). So this
initial all zero part can be windowed out without changing the filter
behaviour. This way the filter becomes almost zero delay, providing a
delay of just ISPELowerWindow samples. This sometimes may be low enough
to make it usable even with home theater systems where audio delay is a
major issue. Of course to ensure that the initial all zero part is
preserved the minimum phase peak limiting should also be used.
  

6.12.2  PSInterpolationType
---------------------------
   
  This parameter defines the type of interpolation used between the
points  of the target transfer function. L means the usual linear
interpolation,  G means logarithmic interpolation, i.e. interpolation
performed on a  bilogarithmic scale, R means interpolation using Uniform
Cubic B  Splines, S means interpolation using Uniform Cubic B Splines on
a  bilogarithmic scale, P means interpolation on a linear scale using a 
monotone Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), H 
means interpolation on a logarithmic scale using PCHIP. The logarithmic 
interpolation makes the definition of the target transfer function 
easier, without the need to define intermediate points to get the 
desired behaviour on a bilogarithmic scale. The default is S. 
  The B Splines interpolation options allow for the definition of smooth
 target transfer functions which provides less ringing. Be careful when 
using this option because defining the right control points to get the 
desired target transfer function might be tricky. B Splines don't 
interpolate the supplied points but are instead tangent to the lines 
connecting the control point. If you want sharp corners in the transfer 
function just place few close control points near to the desired corner.
 Remember that B Splines of the type used are unaffected by control 
points which are more than two control points away from any given point 
on the curve. Take a look at the supplied examples for some simple 
transfer function definition. 
  The PCHIP procedure provides a monotonic interpolation procedure. The 
resulting target is less smooth than the one supplied by B Splines, but 
being a true interpolation PCHIP makes the definition of the control 
points much easier. 
  The use of the B Spline or PCHIP interpolation procedures is often 
useful also for the definition of the mic compensation transfer 
function, especially when only few points are available. 
  

6.12.3  PSMultExponent
----------------------
   
  The multiplier exponent used for the homomorphic deconvolution used to
compute the minimum phase post filter. Usually a value of 2 or 3 is
used.
  

6.12.4  PSFilterLen
-------------------
   
  Length of the FIR filter used during the postfiltering stage. Usually
between 16384 and 65536.
  

6.12.5  PSNumPoints
-------------------
   
  Number of points used for the definition of the post filter frequency
response. If this parameter is 0 DRC automatically counts the number of
lines in the post filter definition file. See the following parameters
for further details about the post filter frequency response.
  

6.12.6  PSMagType
-----------------
   
  This parameter selects how the amplitude of the target frequency
response is defined. L means linear amplitude (0.5 means half the level,
i.e about -6 dB), D means that the amplitude is expressed in dB.
  

6.12.7  PSPointsFile (*)
------------------------
   
  File containing the post filter frequency response definition. This
file should contain PSNumPoints lines, each line in the form "Frequency
Gain", with the gain expressed as a linear gain or in dB depending on
the PSMagType parameter value. The following examples are in dB. The
first line must have a frequency equal to 0, the last line must have a
frequency equal to  BCSampleRate / 2 . A post filter definition file
must have the following format:
    
   <<0 -40
     18 -20
     20 0
     20000 0
     21000 -40
     22050 -100
   >>
   This is for a 44.1 KHz sample rate. 
  The post filter stage is usually used to prevent overcompensation in
the subsonic or ultrasonic range, but may be used also to change the
target frequency response from linear to a more euphonic one.
  Starting from version 2.0.0 DRC lets you specify the phase for the
target post filter stage. Phase specification should be placed after the
amplitude specification and should be expressed in degrees. Following
the example above:
    
   <<0 -40 0
     18 -20 45
     20 0 90
     20000 0 180
     21000 -40 90
     22050 -100 0
   >>
   If not specified a value of 0 is assumed. Setting a phase different
than 0, i.e. flat, is useless within normal HiFi systems in almost all
circumstances. Furthermore the phase specification is used only if the
PSFilterType is L, else any phase specification is wiped out by the
minimum phase filter extraction.
  

6.12.8  PSOutWindow
-------------------
   
  Final window after post filtering. This is also the length of the
generated correction filter. Usual values are between 8192 and 65536.
Filter with 65536 taps gives about 0.5 Hz resolution at 44.1 KHz sample
rate, 16384 is usually enough for most situation and 8192 gives somewhat
good results with much less computing needs during real time
convolution.
  

6.12.9  PSNormFactor
--------------------
   
  Normalization factor for the correction filter. Usually 1.0. See
section 4.6.2 for some instructions on how to set this parameter.
  

6.12.10  PSNormType
-------------------
   
  Normalization type for the correction filter. Usually E. See section
4.6.2 for some instructions on how to set this parameter.
  

6.12.11  PSOutFile
------------------
   
  Output file for the correction filter. This file contains the filter
to be used with the convolution engine.
  

6.12.12  PSOutFileType
----------------------
   
  Output file type for the correction filter. D = Double, F = Float, I =
Integer.
  

6.13  MS - Minimum phase filter extraction Stage
================================================
  
  The minimum phase extraction stage creates a minimum phase filter from
the correction filter. A minimum phase filter corrects just the
magnitude response and the minimum phase part of the phase response, but
it is usually almost artifacts free and as basically zero latency. If
microphone compensation is enabled the filter includes microphone
compensation.
  

6.13.1  MSMultExponent
----------------------
   
  Exponent of the multiplier for the homomorphic deconvolution used to
extract a zero delay minimum phase version of the correction filter. A
value of 2 or 3 is usually enough.
  

6.13.2  MSOutWindow
-------------------
   
  Output window size for the minimum phase filter. Typical values are
about half of PLOutWindow.
  

6.13.3  MSFilterDelay
---------------------
   
  This parameter add an initial delay to the filter, making it possible
to align it with other filters. Usually it is set to the same value
assigned to EPLowerWindow, so that the filter has the same latency of
the mixed phase filter when PSFilterType is set to T. If you want a zero
delay filter set this parameter to 0.
  

6.13.4  MSNormFactor
--------------------
   
  Normalization factor for the minimum phase filter. The same
considerations of section 4.6.2 should be applied.
  

6.13.5  MSNormType
------------------
   
  Normalization type for the minimum phase filter. Usually E. See
section 4.6.2 for some instructions on how to set this parameter.
  

6.13.6  MSOutFile
-----------------
   
  Output file name for the minimum phase filter.
  

6.13.7  MSOutFileType
---------------------
   
  Output file type for the minimum phase filter.
  

6.14  TC - Test Convolution
===========================
  
  

6.14.1  TCNormFactor
--------------------
   
  Normalization factor for the output of the final convolution stage.
Usually 0.0.
  

6.14.2  TCNormType
------------------
   
  Normalization type for the output of the final convolution stage.
Usually E.
  

6.14.3  TCOutFile
-----------------
   
  Output file for the final test convolution. If this is not supplied
the test convolution stage is skipped.
  

6.14.4  TCOutFileType
---------------------
   
  Output type for the file above. D = Double, F = Float, I = Integer.
  

7  Acknowledgments
*=*=*=*=*=*=*=*=*=

  
  DRC grew up with the contribution of many peoples. The list is really
long, and there's some chance that I'm forgetting someone. By the way
here it is the list, in random order:
  
 
 
   - Thanks to Prof. Angelo Farina and Prof. John Mourjopoulos for their
   papers released in the public domain. Many DRC algorithms started
   from references and explanations found in those papers.
 
   - Many thanks to Anders Torger for his BruteFIR package and his
   suggestions. Without BruteFIR DRC would have been just a programming
   exercise, and I would have never started writing it. Anders also gave
   me the idea of the sliding lowpass prefiltering procedure.
 
   - Many thanks to "Jaco the Relentless" for his enthusiastic support
   and for all the tests on his own HiFi system.
 
   - Thanks to Maurizio Mulas for sending me the impulse response of his
   room as a testbed for some releases and for all his listening tests.
 
   - Thanks to Marco Bagna and Alex "Flex" Okely for their support
   during the DRC development and also for letting me testing DRC on
   their high quality HiFi systems.
 
   - Thanks to Michele Spinolo for his enthusiastic support and for
   writing some documentation about DRC and its functionalities.
 
   - Many thanks to "Jones Rush" for all his efforts understanding how
   DRC works and for writing a good step by step DRC guide, something
   that was really missing.
 
   - Many thanks to Tom Browne for his suggestions and tests on his own
   system and his help in optimizing the DRC performances.
 
   - Many thanks to Ed Wildgoose for his suggestions and tests on his
   own system, for providing the perl script which glsweep is based upon
   and for setting up the DRC Wiki pages.
 
   - Thanks to Ulrich "Uli" Brueggemann for providing some filters
   generated with a completely different approach. Most of the changes
   of version 2.5.0 have been implemented after comparing the DRC
   filters with those filters.
 
   - Thanks to Chris Birkinshaw for providing the Jack version of the
   automatic measuring script.
 
   - Thanks to Gregory Maxwell for writing the excellent Wikipedia
   digital room correction article.
 
   - Many thanks to the ALSA team for providing a good Linux sound
   infrastructure and for helping fixing some nasty bugs in the TerraTec
   EWX 24/96 driver.
 
   - Many thanks to the TeX, LaTeX, Octave, GNUPlot and HeVeA developers
   for providing the invaluable tools used to create this document.
   Finally many thanks to all the peoples who have contributed to DRC,
sometimes without even knowing it. Most of the ideas used to develop DRC
come from public papers, algorithms and source code found for free over
the Internet.
  

8  Similar software
*=*=*=*=*=*=*=*=*=*

  
  There are other software packages providing functionalities similar or
 comparable to those of DRC. Here are some examples: 
  
 
 
   - Acourate: http://www.acourate.com/
 
   - Room Eq Wizard: http://www.hometheatershack.com/roomeq/
 
   - Audiolense: http://www.juicehifi.com/
  
  

9  Commercial products
*=*=*=*=*=*=*=*=*=*=*=

  
  A complete commercial package, based on DRC for the filter generation 
procedure, is available from the small Italian company AVA Italy. I have
 no involvement in the development of the product so those interested in
 this package should contact AVA Italy directly. Contact informations
are  available on the AVA Italy web site: 
    http://www.avaitaly.it/ 
  
  
  

A  Sample results
*=*=*=*=*=*=*=*=*

   
  In the following pages some graphs with a comparison between the 
corrected and uncorrected system are reported. This is of course just a 
sample situation and describes what I achieved in my own system. My 
uncorrected system show performance figures which are quite uncommon, 
partly because it is placed in an heavily damped listening room but 
mostly because it has been tuned to give its best with the correction in
 place. So the results for the uncorrected system shouldn't be taken as 
an example of typical behaviour. The results of the corrected system 
show instead the perfomance levels achievable combining active room 
correction with traditional passive room treatment. Depending on the 
behaviour of the speakers and the listening room, and on the settings 
used for DRC, the results could be quite different. 
  The results presented have been obtained with the psychoacoustic
target  stage disabled. All the graphs presented in these section are
based on  traditional objective evaluation of the system transfer
function. No  psychoacoustics is involved in the graphs generation
procedures, so the  results with the psychoacoustic target can't be
evaluated using this  kind of graphs. On the other hand the proposed
graphs clearly show that  the correction is able to closely match the
supplied target, so proving  that any psychoacoustic target computation
would be closely followed by  the correction. This implies that, if the
underlying psychoacoustic  model is correct, the results will be as
expected. 
  All the graphs, except the spectrograms and other 3D plots, follow the
 same conventions. The uncorrected system is reported with red lines and
 the corrected system is reported with blue lines. The spectrograms and 
the 3D plots need a specific colormap for proper visualization, which is
 of course the same for both the corrected and uncorrected system, so 
they can't follow this simple convention. 
  All the graphs have been prepared with the Octave files available
under  the "src/doc/octave" directory of the standard distribution. The 
"createdrcplots.m" file contains a function which creates all the 
graphs needed to compare two impulse responses and saves them into 
encapsulated postscript files or files in any other format supporte by 
Octave. To load the raw pcm files created by DRC you can use the 
"loadpcm" function with some Octave commands like: 
    
   <<ru = loadpcm("/pathtopcm/rmc.pcm");
     rc = loadpcm("/pathtopcm/rtc.pcm");
   >>
    
   The uncorrected response could be obtained by uncommenting the
MCOutFile  parameter and setting it properly. If you don't have a
microphone  compensation file you can simply use the flat target
response to provide  a null compensation and get the needed output file
only. The corrected  response could be obtained by uncommenting the
TCOutFile parameter and  setting it properly. Then the full sets of
graphs will be created with an  Octave command like:
    
   <<createdrcplots(ru,-1,"R Uncorrected",rc,-1,"R
   Corrected","/pathtographs/","R");
   >>
    
  
  Graph in a different format than the standard encapsulated postscript 
may be easily obtained by suppling some further parameters to the 
createdrcplots procedure. For example to create the graphs in PNG format
 a command like this might be used: 
    
   <<createdrcplots(ru,-1,"R Uncorrected",rc,-1,"R
   Corrected","/pathtographs/","R",".png","-dpng");
   >>
    
   All formats supported by the Octave print command may be used. Se the
 Octave documentation for further details. 
  You need at least Octave 3.2.3, along with Octave-Forge and GnuPlot 
version 4.3 or newer, for this script to work. The scripts have been 
tested with octave 3.2.3 and GnuPlot 4.3.0. Octave can be downloaded 
from: 
    http://www.octave.org/ 
  	 Michele Spinolo prepared a LaTeX document which packages the full
set  of graphs into a single file. The LaTeX script is named 
"drc-graphs.tex" and is available under the "src/doc" directory. The 
script could be used for pdf or postscript file creation, or to create 
HTML files using HeVeA, and maybe also wiht Latex2Html. The graphs 
should be created using "T" as the graphs prefix name in the 
"createdrcplots" function above, else you have to edit the header of 
the script to change the graph prefix. HeVeA and Latex2Html are 
available at the following sites: 
    http://www.latex2html.org/
   http://pauillac.inria.fr/~maranget/hevea/ 
   	

A.1  Time response
==================
   
  The first series of graphs show the effect of the correction in the
time domain. The correction provides a clear improvement in the time
response, with an effect that becomes longer and longer in time as the
frequency decrease, as expected.
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-IRStepResponse
    [width=1.0@percent,keepaspectratio]figures/SR-R-IRStepResponse 
  Figure 11:  Corrected and uncorrected step response comparison. The
corrected step response is much closer to the expected exponential decay
than the uncorrected one, at least up to above 10 ms.
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-L-IRFullRange
      [width=1.0@percent,keepaspectratio]figures/SR-R-IRFullRange 
  Figure 12:  Corrected and uncorrected  impulse response comparison.
The corrected impulse response becomes much  similar to a (minimum
phase) bandlimited Dirac spike for about 1 ms.  This implies a close to
perfect phase response at least for the early  direct sound.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-L-IRFullRangeEnvelope
  [width=1.0@percent,keepaspectratio]figures/SR-R-IRFullRangeEnvelope 
  Figure 13:  Impulse response envelope for the corrected and
uncorrected system.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-IRFullRangeETC
    [width=1.0@percent,keepaspectratio]figures/SR-R-IRFullRangeETC 
  Figure 14:  Time-energy response (impulse response envelope plotted
with a logarithmic magnitude scale) for the corrected and uncorrected
system.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-IR2KHzBrickwall
    [width=1.0@percent,keepaspectratio]figures/SR-R-IR2KHzBrickwall 
  Figure 15:  Corrected and uncorrected impulse response comparison. The
impulse responses have been brickwall filtered at 2 KHz to show the
increased effect up to the midrange.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-IR2KHzBrickwallEnvelo
                                   pe
[width=1.0@percent,keepaspectratio]figures/SR-R-IR2KHzBrickwallEnvelope 
  Figure 16:  Impulse response envelope for the corrected and
uncorrected system. The impulse responses have been brickwall filtered
at 2 KHz to show the increased effect up to the midrange.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-L-IR2KHzBrickwallETC
  [width=1.0@percent,keepaspectratio]figures/SR-R-IR2KHzBrickwallETC 
  Figure 17:  Time-energy response (impulse response envelope plotted
with a logarithmic magnitude scale) for the corrected and uncorrected
system. The impulse responses have been brickwall filtered at 2 KHz to
show the increased effect up to the midrange.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-IR200HzBrickwall
   [width=1.0@percent,keepaspectratio]figures/SR-R-IR200HzBrickwall 
  Figure 18:  Corrected and uncorrected impulse response comparison. The
impulse responses have been brickwall filtered at 200 Hz to show the
further increased effect in the bassrange.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-IR200HzBrickwallEnvel
                                  ope
[width=1.0@percent,keepaspectratio]figures/SR-R-IR200HzBrickwallEnvelope
Figure 19:  Impulse response envelope for the corrected and uncorrected
system. The impulse responses have been brickwall filtered at 200 Hz to
show the further increased effect in the bassrange.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-L-IR200HzBrickwallETC
  [width=1.0@percent,keepaspectratio]figures/SR-R-IR200HzBrickwallETC 
  Figure 20:  Time-energy response (impulse response envelope plotted
with a logarithmic magnitude scale) for the corrected and uncorrected
system. The impulse responses have been brickwall filtered at 200 Hz to
show the further increased effect in the bassrange.
                                     
   
        --------------------------------------------------------
  
  

A.2  Frequency response
=======================
   
  These series of graphs show the effect of the correction on the
frequency response magnitude for some different windows applied to the
time response and with different kind of smoothing applied.
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-MRUnsmoothed1ms
    [width=1.0@percent,keepaspectratio]figures/SR-R-MRUnsmoothed1ms 
  Figure 21:  Unsmoothed frequency response magnitude, 1 ms Blackman
window. These graphs show the frequency response of the early direct
sound.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-MRUnsmoothed5ms
    [width=1.0@percent,keepaspectratio]figures/SR-R-MRUnsmoothed5ms 
  Figure 22:  Unsmoothed frequency response magnitude, 5 ms Blackman
window. These graphs show the frequency response of the direct sound.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-MRUnsmoothed200ms
   [width=1.0@percent,keepaspectratio]figures/SR-R-MRUnsmoothed200ms 
  Figure 23:  Unsmoothed frequency response magnitude, bass range, 200
ms Blackman window. These graphs show the frequency response of the bass
range over a 200 ms time window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-MRFDWSmoothed
     [width=1.0@percent,keepaspectratio]figures/SR-R-MRFDWSmoothed 
  Figure 24:  Frequency response magnitude smoothed using a frequency
dependent windowing with windowing settings close to those used by the
normal.drc sample configuration file.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-MRFDWSmoothed-1-6
   [width=1.0@percent,keepaspectratio]figures/SR-R-MRFDWSmoothed-1-6 
  Figure 25:  Frequency response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/6 of
octave smoothing.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-MRFDWSmoothed-1-3
   [width=1.0@percent,keepaspectratio]figures/SR-R-MRFDWSmoothed-1-3 
  Figure 26:  Frequency response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/3 of
octave smoothing.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-MRBarkSmoothed
    [width=1.0@percent,keepaspectratio]figures/SR-R-MRBarkSmoothed 
  Figure 27:  Frequency response magnitude  smoothed over the Bark
psychoacoustic scale with many different Blackman windows applied.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-MRERBSmoothed
     [width=1.0@percent,keepaspectratio]figures/SR-R-MRERBSmoothed 
  Figure 28:  Frequency response magnitude  smoothed the ERB
psychoacoustic scale with many different Blackman windows applied.
                                     
   
        --------------------------------------------------------
  
  

A.3  Phase response
===================
   
  This section show some phase response graphs. The phase response
becomes basicly linear at least for the direct sound, which implies also
a constant group delay.
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-PRUnsmoothed1ms
    [width=1.0@percent,keepaspectratio]figures/SR-R-PRUnsmoothed1ms 
  Figure 29:  Unsmoothed phase response, 1 ms Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-L-PRUnsmoothed5ms
    [width=1.0@percent,keepaspectratio]figures/SR-R-PRUnsmoothed5ms 
  Figure 30:  Unsmoothed phase response, 5 ms Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-PRUnsmoothed200ms
   [width=1.0@percent,keepaspectratio]figures/SR-R-PRUnsmoothed200ms 
  Figure 31:  Unsmoothed phase response, bass range, 200 ms Blackman
window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-PRFDWSmoothed
     [width=1.0@percent,keepaspectratio]figures/SR-R-PRFDWSmoothed 
  Figure 32:  Phase response smoothed using a frequency dependent
windowing with windowing settings close to those used by the normal.drc
sample configuration file.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-PRFDWSmoothed-1-6
   [width=1.0@percent,keepaspectratio]figures/SR-R-PRFDWSmoothed-1-6 
  Figure 33:  Phase response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/6 of
octave smoothing.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-PRFDWSmoothed-1-3
   [width=1.0@percent,keepaspectratio]figures/SR-R-PRFDWSmoothed-1-3 
  Figure 34:  Phase response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/3 of
octave smoothing.
                                     
   
        --------------------------------------------------------
  
  

A.4  Time-frequency analysis
============================
   
  In this section some joint time-frequency analysis results are
presented. Time-frequency graphs are more difficult to understand than
the graphs presented so far, but they provide also invaluable
information about how the system under test is working. The human ear
works using a joint time-frequency analysis too, so these graphs provide
a representation of the system behaviour that is much closer to our
subjective perception.
  Many graphs show the spectral decay of the system. The spectral decay
isn't exactly the same as the cumulative spectral decay (CSD) often used
for loudspeaker analysis, even though it is strictly related to it. The
spectral decay is obtained using an oversampled short-time Fourier
transform of the impulse response, being careful to use a window that is
long enough to satisfy the Gabor inequality (see section 4.2 and figure
5 for details).
  The correct interpretation of the graphs presented in this section
would require a book by itself, so little words are spent describing the
results achieved. With respect to this any comment is welcome.
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SDHighRange 
  Figure 35:  Left channel, spectral decay, high range. Spectral decay
from 2 KHz to 20 KHz with a 0.5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SDHighRange 
  Figure 36:  Right channel, spectral decay, high range. Spectral decay
from 2 KHz to 20 KHz with a 0.5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SFHighRange 
  Figure 37:  Left channel, spectral formation, high range. Spectral
formation from 2 KHz to 20 KHz with a 0.5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SFHighRange 
  Figure 38:  Right channel, spectral formation, high range. Spectral
formation from 2 KHz to 20 KHz with a 0.5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-L-SDMidRange 
  Figure 39:  Left channel, spectral decay, mid range. Spectral decay
from 200 Hz to 2000 Hz with a 5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-R-SDMidRange 
  Figure 40:  Right channel, spectral decay, mid range. Spectral decay
from 200 Hz to 2000 Hz with a 5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-L-SFMidRange 
  Figure 41:  Left channel, spectral formation, mid range. Spectral
formation from 200 Hz to 2000 Hz with a 5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-R-SFMidRange 
  Figure 42:  Right channel, spectral formation, mid range. Spectral
formation from 200 Hz to 2000 Hz with a 5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SDBassRange 
  Figure 43:  Left channel, spectral decay, bass range. Spectral decay
from 20 Hz to 200 Hz with a 50 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SDBassRange 
  Figure 44:  Right channel, spectral decay, bass range. Spectral decay
from 20 Hz to 200 Hz with a 50 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SFBassRange 
  Figure 45:  Left channel, spectral formation, bass range. Spectral
formation from 20 Hz to 200 Hz with a 50 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SFBassRange 
  Figure 46:  Right channel, spectral formation, bass range. Spectral
formation from 20 Hz to 200 Hz with a 50 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SDHighRangeW 
  Figure 47:  Left channel, spectral decay, high range. Spectral decay
from 2 KHz to 20 KHz with a 1.0 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SDHighRangeW 
  Figure 48:  Right channel, spectral decay, high range. Spectral decay
from 2 KHz to 20 KHz with a 1.0 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SFHighRangeW 
  Figure 49:  Left channel, spectral formation, high range. Spectral
formation from 2 KHz to 20 KHz with a 1.0 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SFHighRangeW 
  Figure 50:  Right channel, spectral formation, high range. Spectral
formation from 2 KHz to 20 KHz with a 1.0 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SDMidRangeW 
  Figure 51:  Left channel, spectral decay, mid range. Spectral decay
from 200 Hz to 2000 Hz with a 10 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SDMidRangeW 
  Figure 52:  Right channel, spectral decay, mid range. Spectral decay
from 200 Hz to 2000 Hz with a 10 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SFMidRangeW 
  Figure 53:  Left channel, spectral formation, mid range. Spectral
formation from 200 Hz to 2000 Hz with a 10 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SFMidRangeW 
  Figure 54:  Right channel, spectral formation, mid range. Spectral
formation from 200 Hz to 2000 Hz with a 10 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SDBassRangeW 
  Figure 55:  Left channel, spectral decay, bass range. Spectral decay
from 20 Hz to 200 Hz with a 100 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SDBassRangeW 
  Figure 56:  Right channel, spectral decay, bass range. Spectral decay
from 20 Hz to 200 Hz with a 100 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-L-SFBassRangeW 
  Figure 57:  Left channel, spectral formation, bass range. Spectral
formation from 20 Hz to 200 Hz with a 100 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-R-SFBassRangeW 
  Figure 58:  Right channel, spectral formation, bass range. Spectral
formation from 20 Hz to 200 Hz with a 100 ms sliding Blackman window. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-Spectrogram01ms 
  Figure 59:  High resolution spectrograms  from -10 ms to 40 ms, 1 ms
Blackman window, 90 dB level range, left  channel. The frequency range
is from DC to the Nyquist frequency (22050  Hz) on a linear scale. The
uncorrected system is on the top and the  corrected system is on the
bottom.
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-R-Spectrogram01ms 
  Figure 60:  High resolution spectrograms  from -10 ms to 40 ms, 1 ms
Blackman window, 90 dB level range, right  channel. The frequency range
is from DC to the Nyquist frequency (22050  Hz) on a linear scale. The
uncorrected system is on the top and the  corrected system is on the
bottom.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-L-Spectrogram20ms 
  Figure 61:  High resolution spectrograms  from -100 ms to 400 ms, 20
ms Blackman window, 90 dB level range, left  channel. The frequency
range is from DC to the Nyquist frequency (22050  Hz) on a linear scale.
The uncorrected system is on the top and the  corrected system is on the
bottom.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-R-Spectrogram20ms 
  Figure 62:  High resolution spectrograms  from -100 ms to 400 ms, 20
ms Blackman window, 90 dB level range, right  channel. The frequency
range is from DC to the Nyquist frequency (22050  Hz) on a linear scale.
The uncorrected system is on the top and the  corrected system is on the
bottom.
                                     
   
        --------------------------------------------------------
  
  

A.5  Wavelet cycle-octave analysis
==================================
   
  The wavelet analysis is a different method for performing a
time-frequency analysis or, to be precise, a time-scale analysis. For
certain kind of wavelets the scale axis could be mapped to a frequency
scale, allowing for the usual time-frequency interpretation of the
time-scale plots.
  Wavelets have the advantage of being easier to map to a logarithmic
frequency scale. To further help the correct interpretation of the
graphs the time scale is also stretched, depending on the frequency, so
that the time scale is expressed in cycles of the sine wave of the
corresponding frequency. The end result is a graph that provides a
tiling of the time-frequency plane which is visually quite close to the
kind of time-frequency analysis performed by our auditory system.
  The graphs are classical cycle-octave scalograms based on the Morlet 
wavelet, tuned for different tradeoffs between time and frequency 
resolution. 
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramHTRENV
                                  SD 
  Figure 63:  Left channel, Morlet  cycle-octave scalogram envelope,
high time resolution, spectral decay. 
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramHTRENV
                                  SD 
  Figure 64:  Right channel, Morlet  cycle-octave scalogram envelope,
high time resolution, spectral decay. 
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramHTRENV
                                  SF 
  Figure 65:  Left channel, Morlet  cycle-octave scalogram envelope,
high time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramHTRENV
                                  SF 
  Figure 66:  Right channel, Morlet  cycle-octave scalogram envelope,
high time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramHTRENV
                                  Map 
  Figure 67:  Left channel, Morlet  cycle-octave scalogram envelope,
high time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramHTRENV
                                  Map 
  Figure 68:  Right channel, Morlet  cycle-octave scalogram envelope,
high time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramHTRETC
                                  SD 
  Figure 69:  Left channel, Morlet  cycle-octave scalogram ETC, high
time resolution, spectral decay. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramHTRETC
                                  SD 
  Figure 70:  Right channel, Morlet  cycle-octave scalogram ETC, high
time resolution, spectral decay. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramHTRETC
                                  SF 
  Figure 71:  Left channel, Morlet  cycle-octave scalogram ETC, high
time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramHTRETC
                                  SF 
  Figure 72:  Right channel, Morlet  cycle-octave scalogram ETC, high
time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramHTRETC
                                  Map 
  Figure 73:  Left channel, Morlet  cycle-octave scalogram ETC, high
time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramHTRETC
                                  Map 
  Figure 74:  Right channel, Morlet  cycle-octave scalogram ETC, high
time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramMTRENV
                                  SD 
  Figure 75:  Left channel, Morlet  cycle-octave scalogram envelope,
medium time resolution, spectral decay. 
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramMTRENV
                                  SD 
  Figure 76:  Right channel, Morlet  cycle-octave scalogram envelope,
medium time resolution, spectral decay. 
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramMTRENV
                                  SF 
  Figure 77:  Left channel, Morlet  cycle-octave scalogram envelope,
medium time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramMTRENV
                                  SF 
  Figure 78:  Right channel, Morlet  cycle-octave scalogram envelope,
medium time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramMTRENV
                                  Map 
  Figure 79:  Left channel, Morlet  cycle-octave scalogram envelope,
medium time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramMTRENV
                                  Map 
  Figure 80:  Right channel, Morlet  cycle-octave scalogram envelope,
medium time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramMTRETC
                                  SD 
  Figure 81:  Left channel, Morlet  cycle-octave scalogram ETC, medium
time resolution, spectral decay. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramMTRETC
                                  SD 
  Figure 82:  Right channel, Morlet  cycle-octave scalogram ETC, medium
time resolution, spectral decay. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramMTRETC
                                  SF 
  Figure 83:  Left channel, Morlet  cycle-octave scalogram ETC, medium
time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramMTRETC
                                  SF 
  Figure 84:  Right channel, Morlet  cycle-octave scalogram ETC, medium
time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-L-MorletScalogramMTRETC
                                  Map 
  Figure 85:  Left channel, Morlet  cycle-octave scalogram ETC, medium
time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-R-MorletScalogramMTRETC
                                  Map 
  Figure 86:  Right channel, Morlet  cycle-octave scalogram ETC, medium
time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
  

A.6  Baseline
=============
   
  The following series of graphs show the comparison between a Dirac
delta and the corrected left channel. The Dirac delta is the
mathematical representation of a "perfect" system i.e. a system which
outputs a perfect copy of its input. Looking at these graphs it is
possible to see both what is left uncorrected by DRC and what a
"perfect" system looks like on this kind of graphs. The graphs are
presented in the same order of the previous graphs.
  

A.6.1  Baseline time response
-----------------------------
    
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-B-IRStepResponse 
  Figure 87:  Step response
       [width=1.0@percent,keepaspectratio]figures/SR-B-IRFullRange 
  Figure 88:  Full range impulse response.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-IRFullRangeEnvelope 
  Figure 89:  Full range impulse response envelope.
      [width=1.0@percent,keepaspectratio]figures/SR-B-IRFullRangeETC 
  Figure 90: Full range time-energy response.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-B-IR2KHzBrickwall 
  Figure 91:  Impulse response after brickwall filtering at 2 KHz.
   [width=1.0@percent,keepaspectratio]figures/SR-B-IR2KHzBrickwallEnvelo
                                  pe 
  Figure 92:  Impulse response envelope after brickwall filtering at 2
KHz.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-B-IR2KHzBrickwallETC 
  Figure 93:  Time-energy response after brickwall filtering at 2 KHz.
     [width=1.0@percent,keepaspectratio]figures/SR-B-IR200HzBrickwall 
  Figure 94:  Impulse response after brickwall filtering at 200 Hz.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-IR200HzBrickwallEnvel
                                  ope 
  Figure 95:  Impulse response envelope after brickwall filtering at 200
Hz.
   [width=1.0@percent,keepaspectratio]figures/SR-B-IR200HzBrickwallETC 
  Figure 96:  Time-energy response after brickwall filtering at 200 Hz.
                                     
   
        --------------------------------------------------------
  
  

A.6.2  Baseline frequency response
----------------------------------
    
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-B-MRUnsmoothed1ms 
  Figure 97:  Unsmoothed frequency response magnitude, 1 ms Blackman
window.
     [width=1.0@percent,keepaspectratio]figures/SR-B-MRUnsmoothed5ms 
  Figure 98:  Unsmoothed frequency response magnitude, 5 ms Blackman
window.
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-B-MRUnsmoothed200ms 
  Figure 99:  Unsmoothed frequency response magnitude, bass range, 200
ms Blackman window.
      [width=1.0@percent,keepaspectratio]figures/SR-B-MRFDWSmoothed 
  Figure 100:  Frequency response magnitude smoothed using a frequency
dependent windowing with windowing settings close to those used by the
normal.drc sample configuration file.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-B-MRFDWSmoothed-1-6 
  Figure 101:  Frequency response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/6 of
octave smoothing.
    [width=1.0@percent,keepaspectratio]figures/SR-B-MRFDWSmoothed-1-3 
  Figure 102:  Frequency response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/3 of
octave smoothing.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
      [width=1.0@percent,keepaspectratio]figures/SR-B-MRBarkSmoothed 
  Figure 103:  Frequency response  magnitude smoothed over the Bark
psychoacoustic scale with many different Blackman windows applied.
       [width=1.0@percent,keepaspectratio]figures/SR-B-MRERBSmoothed 
  Figure 104:  Frequency response  magnitude smoothed over the Bark
psychoacoustic scale with many different Blackman windows applied.
                                      
   
        --------------------------------------------------------
  
  

A.6.3  Baseline phase response
------------------------------
    
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-B-PRUnsmoothed1ms 
  Figure 105:  Unsmoothed phase response, 1 ms Blackman window.
     [width=1.0@percent,keepaspectratio]figures/SR-B-PRUnsmoothed5ms 
  Figure 106:  Unsmoothed phase response, 5 ms Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-B-PRUnsmoothed200ms 
  Figure 107:  Unsmoothed phase response, 200 ms Blackman window.
      [width=1.0@percent,keepaspectratio]figures/SR-B-PRFDWSmoothed 
  Figure 108:  Phase response smoothed using a frequency dependent
windowing with windowing settings close to those used by the normal.drc
sample configuration file.
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
    [width=1.0@percent,keepaspectratio]figures/SR-B-PRFDWSmoothed-1-6 
  Figure 109:  Phase response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/6 of
octave smoothing.
    [width=1.0@percent,keepaspectratio]figures/SR-B-PRFDWSmoothed-1-3 
  Figure 110:  Phase response magnitude smoothed using a frequency
dependent windowing providing a frequency resolution close to 1/3 of
octave smoothing.
                                     
   
        --------------------------------------------------------
  
  

A.6.4  Baseline time-frequency analysis
---------------------------------------
    
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SDHighRange 
  Figure 111:  Left channel, spectral decay, high range. Spectral decay
from 2 KHz to 20 KHz with a 0.5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SFHighRange 
  Figure 112:  Left channel, spectral formation, high range. Spectral
formation from 2 KHz to 20 KHz with a 0.5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-B-SDMidRange 
  Figure 113:  Left channel, spectral decay, mid range. Spectral decay
from 200 Hz to 2000 Hz with a 5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
        [width=1.0@percent,keepaspectratio]figures/SR-B-SFMidRange 
  Figure 114:  Left channel, spectral formation, mid range. Spectral
formation from 200 Hz to 2000 Hz with a 5 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SDBassRange 
  Figure 115:  Left channel, spectral decay, bass range. Spectral decay
from 20 Hz to 200 Hz with a 50 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SFBassRange 
  Figure 116:  Left channel, spectral formation, bass range. Spectral
formation from 20 Hz to 200 Hz with a 50 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SDHighRangeW 
  Figure 117:  Left channel, spectral decay, high range. Spectral decay
from 2 KHz to 20 KHz with a 1.0 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SFHighRangeW 
  Figure 118:  Left channel, spectral formation, high range. Spectral
formation from 2 KHz to 20 KHz with a 1.0 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SDMidRangeW 
  Figure 119:  Left channel, spectral decay, mid range. Spectral decay
from 200 Hz to 2000 Hz with a 10 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SFMidRangeW 
  Figure 120:  Left channel, spectral formation, mid range. Spectral
formation from 200 Hz to 2000 Hz with a 10 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SDBassRangeW 
  Figure 121:  Left channel, spectral decay, bass range. Spectral decay
from 20 Hz to 200 Hz with a 50 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
       [width=1.0@percent,keepaspectratio]figures/SR-B-SFBassRangeW 
  Figure 122:  Left channel, spectral formation, bass range. Spectral
formation from 20 Hz to 200 Hz with a 100 ms sliding Blackman window.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-B-Spectrogram01ms 
  Figure 123:  High resolution spectrograms from -10 ms to 40 ms, 1 ms
Blackman window, 90 dB level range, left channel. The frequency range is
from DC to Nyquist (22050 Hz) on a linear scale.
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
     [width=1.0@percent,keepaspectratio]figures/SR-B-Spectrogram20ms 
  Figure 124:  High resolution spectrograms from -100 ms to 400 ms, 20
ms Blackman window, 90 dB level range, left channel. The frequency range
is from DC to Nyquist (22050 Hz) on a linear scale.
                                     
   
        --------------------------------------------------------
  
  

A.6.5  Baseline wavelet cycle-octave analysis
---------------------------------------------
   
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramHTRENV
                                  SD 
  Figure 125:  Baseline, Morlet  cycle-octave scalogram envelope, high
time resolution, spectral decay. 
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramHTRENV
                                  SF 
  Figure 126:  Baseline, Morlet  cycle-octave scalogram envelope, high
time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramHTRENV
                                  Map 
  Figure 127:  Baseline, Morlet  cycle-octave scalogram envelope, high
time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramHTRETC
                                  SD 
  Figure 128:  Baseline, Morlet  cycle-octave scalogram ETC, high time
resolution, spectral decay. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramHTRETC
                                  SF 
  Figure 129:  Baseline, Morlet  cycle-octave scalogram ETC, high time
resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramHTRETC
                                  Map 
  Figure 130:  Baseline, Morlet  cycle-octave scalogram ETC, high time
resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramMTRENV
                                  SD 
  Figure 131:  Baseline, Morlet  cycle-octave scalogram envelope, medium
time resolution, spectral decay. 
                                      
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramMTRENV
                                  SF 
  Figure 132:  Baseline, Morlet  cycle-octave scalogram envelope, medium
time resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramMTRENV
                                  Map 
  Figure 133:  Baseline, Morlet  cycle-octave scalogram envelope, medium
time resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramMTRETC
                                  SD 
  Figure 134:  Baseline, Morlet  cycle-octave scalogram ETC, medium time
resolution, spectral decay. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramMTRETC
                                  SF 
  Figure 135:  Baseline, Morlet  cycle-octave scalogram ETC, medium time
resolution, spectral formation. 
                                     
   
        --------------------------------------------------------
  
        --------------------------------------------------------
   
   [width=1.0@percent,keepaspectratio]figures/SR-B-MorletScalogramMTRETC
                                  Map 
  Figure 136:  Baseline, Morlet  cycle-octave scalogram ETC, medium time
resolution, colored map. 
                                     
   
        --------------------------------------------------------
  
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