[Clam-devel] residual spectrum line segment approximation?

Xavier Amatriain xavier at amatriain.net
Thu Aug 7 14:18:05 PDT 2008

Hi Baba,

Sorry for the late response but I think that this discussion is getting 
a bit off-topic for this mailing list as it is more a discussion on DSP 
issues than on CLAM itself. I encourage you  to take the thread to the 
music-dsp mailing list [1] where you will probably get much more (and 
quicker) feedback on general DSP questions... Unfortunately I don't have 
as much time as I wished to get to these questions that require more 
thinking than writing ;-)

In any case, I don't see anything fundamentally wrong in your procedure 
except in the way you have decided on the input spectrum. The idea 
behind applying the BH92 to the residual spectrum was because when doing 
the line approximation out of few spectral points you are "losing" the 
effect of the analysis window. It is similar to what happens when you  
do the peak detection process in the sinusoidal component. If you use 
the original spectrum you are in fact applying the window twice, right? 
Or am I missing something? As a quick test you could try doing a peak 
detection + sinusoidal synthesis (without phase continuation) also on 
the residual component. This should mimic the effect of what I was 
proposing... more or less.

Also, what do you exactly mean when you mention phase discontinuities? 
Could you post some audio examples somewhere? Listening to the result 
can sometimes save a few lines of email text :-)


[1] http://music.columbia.edu/mailman/listinfo/music-dsp

roumbaba wrote:
> So I have *not* managed to correctly apply the bh92 window to my 
> modified residual spectrum and thus I have *not* eliminate phase 
> discontinuities at resynth time.
> One thing i still do not understand is why SMS need odd analysis 
> window sizes and how I should handle this. I specify analysis window 
> size to be 1024 and internally it seems to become 1025 and my 1STF 
> frames are 513 in size. The fact that i do not understand that issue 
> might be one of the source of what I do not do right.
> Here is where I am at so far. Any hint on what I do wrong or should do 
> otherwise is welcome of course:
> - For testing purpose the only modification I do to the original 513 
> values of the noise spectrum is to randomize phases.
> - Then I expand the 513 spectrum to a 1026 spectrum by an even symetry 
> across the 513.5 axis and complex conjugate of the last 513 values.
> - Then I do a circular convolution of my 1026 spectrum with the FFT of 
> a  1026 bh92time window.
>     the way I compute the bh92  time window is (matlab code for now):
>         w1Length = 1026;
>         fConst=2*pi/(w1Length+1-1);
>         w1=[1:w1Length];
>         w1=.35875 -.48829*cos(fConst*w1)+.14128*cos(fConst*2*w1) 
> -.01168*cos(fConst*3*w1);
> - When I check the real  part (and the magnitude)  of the ifft of the 
> resulting 1026 values spectrum resulting of the convolutiong, I do see 
> that the windowing worked and that the resulting time signal smoothes 
> to 0 at begining and end.
> - Then I take the first 513 values of the resulting spectrum and 
> replace the corresponding 1STF frame in the original sdif analysis file
> Still I get phase discontinuites in the resynth signal.
> What am i missing?
> Thanks,
> Baba
> On 15 juil. 08, at 14:55, Xavier Amatriain wrote:
>> Hi Roumbaba, and congrats for your progress!
>> You are right on the source of your problem: SMSSynthesis expects 
>> your residual to come with an analysis window and if not things are 
>> likely to mess up.
>> The lines that are "guilty" for that are around SMSSynthesis.cxx:252
>> http://clam.iua.upf.edu/doc/CLAM-doxygen/SMSSynthesis_8cxx-source.html#l00252 
>> First the peaks are synthesized into a sinusoidal spectrum. Then the 
>> two spectrums are added. Already at that point the spectrums are 
>> supposed to have the same analysis window (BH92) and size. The effect 
>> of that window is undone in line 261 when the global spectral 
>> synthesis is performed.
>> The issue here is that you need to guarantee that both spectrum come 
>> from a similar place before adding them... The sinusoidal peaks are 
>> reconstructed by convolving by the transform of the main lobe of the 
>> window (BH92) but you are reconstructing the residual in a different 
>> way. So.... you either apply the BH92 transform to your spectrum or 
>> avoid doing that in the peak synthesis (and then avoid multiplying by 
>> the inverse in the global spectral synthesis). None of the two 
>> options are immediate but I'd say the first one should be easier to 
>> work out.
>> Hope it helps... and if you get it to work don't forget to report back.
>> roumbaba wrote:
>>> Hello all and thanks again for your previous help,
>>> So I have written some matlab script to perform noise spectrum line 
>>> segment approximation.
>>> - As input the script  takes  an sdif file generated by analysis 
>>> with  SMSConsole.
>>> - It then reads all sdif frames, in particular the 1STF frames 
>>> containing the noise spectrums in complex form.
>>> - It converts these complex spectrums into magPhase form
>>> - It performs line segment approximation on the amplitudes.
>>> To check the impact of the approximation on the quality of  
>>> resynthesis the script does the following:
>>> - It  reconstructs  full noise magnitude spectrums from the line 
>>> approximations  (by linear interpolation)
>>> - It randomizes the phases
>>> - It converts the new "smoothed" magPhase spectrums back to complex 
>>> spectrums
>>> - It writes back  the sdif file with these new "smoothed" spectrums 
>>> instead of the original raw noise spectrums.
>>> Then I run SMSConsole to synthesize that sdif file with the exact 
>>> same parameters than for the original sdif file.
>>> My problem is that the resulting synthesised noise sounds like 
>>> something is wrong in the synthesis overlap-add (like lots of 
>>> discontinuites in the resynthesis)
>>> I think that this might be due to what is described in  the 
>>> Serra/Smith 1990 CMJ paper concerning line segment approximation 
>>> noise resynthesis:
>>> " ...Since the [new] phase spectrum used is not the result of an 
>>> analysis process (with windowing of a waveform, zero padding, and 
>>> FFT computation), the resulting signal does not tapper to 0 at the 
>>> boundaries. This is because a phase spectrum with random values 
>>> corresponds to a phase spectrum of a rectangular-windowed noise 
>>> waveform of size N. In order to succeed in the overlap-add 
>>> resynthesis (ie, to obtain smooth transitions between frames) we 
>>> need a smoothly windowed waveform of size M, where M is the 
>>> synthesis-window length. ....
>>> "
>>> So what might be happening is that by default SMSConsole assumes 
>>> that the 1STF frames are *NOT* line segment approximation and 
>>> therefore does *NOT* perform that last windowing at synthesis time. 
>>> I have gone a little bit through SMS/Clam code but I cannot find 
>>> where I can change this behavior or even if that is the default 
>>> behavior. Where shoud I look in the SMS/Clam code?
>>> Thanks,
>>> Roumbaba
>>> On 27 mai 08, at 23:25, Xavier Amatriain wrote:
>>>> Hi Roumbaba,
>>>> In the paper you cite it says "you can", which does not mean "you 
>>>> have to" :-) Doing an approximation of the residual model is indeed
>>>> an interesting thing to do, especially if you want to reduce the 
>>>> amount of data in your transformed signal, however it is not a must.
>>>> Note that there are many other ways to model the residual apart 
>>>> from the one mentioned in that paper.
>>>> So far, in CLAM we are using the residual as is, with no modeling 
>>>> or approximation. The "only" downside is that the transformed
>>>> signal (SMS Data) is in fact larger than the original audio when it 
>>>> could be much smaller with not much loss in quality. If for
>>>> whatever reason you do need to do the residual modeling you can 
>>>> look at the SpectralEnvelopeExtract processing. This processing
>>>> generates a spectral approximation (spectrum in bpf format) but 
>>>> from an array of peaks, it would not be hard to modify it to work
>>>> with an input spectrum.
>>>> X
>>>> roumbaba wrote:
>>>>> Hi all,
>>>>> I am trying to understand how the residual spectrum gets modeled 
>>>>> in clam/SMS. I have read the Serra/Smith 1990 CMJ paper and as I 
>>>>> understand it  it describes two steps:
>>>>> 1- substract the harmonic spectrum from the original spectrum
>>>>> 2- perform a line-segment approximation of the residual spectrum 
>>>>> obtained in 1
>>>>> I have stepped through clam and SMS code and I think I can see 
>>>>> where step 1 gets performed:
>>>>> SMSAnalysisCore::Do()
>>>>> {
>>>>> mSinSpectralAnalysis.Do();
>>>>> mResSpectralAnalysis.Do();
>>>>> ...
>>>>> ...
>>>>> ...
>>>>> mSynthSineSpectrum.Do();
>>>>> mSpecSubstracter.Do(); /* step 1 gets performed here I think*/
>>>>> }
>>>>> but I cannot find where step 2 (line approximation) gets 
>>>>> performed. Where should I look in the code?
>>>>> Thank you very much,
>>>>> Cheers,
>>>>> Roumbaba
>>>>> ps:
>>>>> Here is a quote from the paper I mentionned above:
>>>>> "Approximation of the Spectral Residual
>>>>> Assuming the the residual signal is quasi-stochastic, each 
>>>>> magnitude-spectrum residual can be approximated by its envelope 
>>>>> since only its shape contributes to the sound characteristics. 
>>>>> [...] The particular line-segment approximation performed here is 
>>>>> done by stepping through the magnitude spectrum and finding local 
>>>>> maxima in every section, ..."
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