[Clam-devel] residual spectrum line segment approximation?

roumbaba roumbaba at gmail.com
Fri Aug 8 17:16:08 PDT 2008

Hi Xavier, and thank you for you reply,

I will ask this question to another forum as you suggest. One  
question though that another forum might not be able to address is  
how specifically SMS internally deals with the analysis window size:  
When I specify an analysis window of 1024 I get 1STF frames of  
windowsize 1025 and fft size 513. What happens internally?

Anyhow, I actually have tried different input spectrums

	- the original spectrum with phase randomization
	- the original spectrum subsampled (in frequency domain) then  
linearly interpolated to reconstruct it with its full number of values.

I always get the same type of audio results which I suspect might be  
due to the way I choose window sizes and what I do with that 513th  
Following your recommendations today I also  did some trys where I   
"deconvolved"  the effect of the original analysis window before I  
even do the linear subsampling (or the phase randomization). Still I  
get the same type of artifacts which actually are not "phase  
discontinuities" as I wrongly stated in my previous message. (What I  
meant by that was clicks caused by discontinuities in the synthesized  
audio signal ). In fact the artifacts now is that the resynthesized  
signal seems to be composed of "packets" or "wavelet kernels" which  
seems to indicate that the overlap add is wrong somewhere, or that my  
window shapes are off or something.

I agree that a short sound can save lines of text. I have 4 audio  
examples (about 184Kb each) that I can send to you directly to avoid  
sending it to the whole list. (I don't have a place to post it unless  
you know of one.)

1- the interpolated noise spectrum resynth with convolution by bh92  
in freq domain to compensate for the 'lost' window
2- the interpolated noise spectrum resynth without convolution:
3- the original noise spectrum resynth:  
4- the original noise spectrum resynth with convolution of bh92 in  
spec domain (window applied twice but sound more or less ok as  
opposed to 1 and 2)

Thank you again for your time,


On 7 août 08, at 14:18, Xavier Amatriain wrote:

> 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 :-)
> X
> [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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