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Weighed overlap add Filterbank structure is often used in speech coding. (https://www.onsemi.com/site/pdf/Filtering_Hearing_Ai.pdf)

I have basic question with respect to analysis.

what is the difference conceptually between:

a) direct analysis: e.g La=R=N1=256 This includes:

  1. extract R=La samples of frame from speech
  2. window it with window of length R=N1
  3. compute its R=N1, point FFT

vs
b) WOLA( let La=256 = 8*32=>k=8,N1=32, R=16 . the diagram for this is:
enter image description here
1.Extract R samples of speech( R'<'N1)
2. Put these into FIFO of length La= k*N1
3. window this by window of length La samples
4. divide the buffer into k buffers, each of length N1
5. add the buffers
6. compute (block_no)mod(R) circular shift of buffer
7. compute N1 point FFT

If the input was a delta function, after analysis, what would be the difference in frequency response of the system(or the window) and what advantage we get by doing WOLA?

thanks for any help that i can get
sedy

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  • $\begingroup$ WOLA allows you to use an N-point DFT with an MN-point analysis window. M, N, and the window shape collectively give you an additional degree of freedom over your approach (a) when designing the frequency response of the system. This can give you, for example, reduced correlation between the analysis bins so that frequency-domain modifications to one bin have a lesser influence on adjacent bins -- which can be important if your input includes narrowband content to be excised or enhanced. $\endgroup$
    – John
    Sep 16 '14 at 12:30
  • $\begingroup$ Thanks John. As I understand now, normally, a N point FFT on M*N point signal would mean time-aliasing in the time domain.However, I have read that stack and add operation( 4 and 5 above) cancels that, and then, the benefit of longer windowing would come in , as indicated by you. But, how does this stack and add operation cancel the time-domain aliasing? or is it that stack and add during analysis and periodic repetition during synthesis cancels it? thanks $\endgroup$
    – user915783
    Sep 17 '14 at 16:33
  • $\begingroup$ Stack and add is time aliasing -- folding windowed time data back onto itself. In synthesis, you replicate the N-point IFFT result and window it. So long as the window has certain properties (and you de-overlap properly just like a non-WOLA scheme), you can get perfect reconstruction. $\endgroup$
    – John
    Sep 17 '14 at 16:48
  • $\begingroup$ Hi John, Thanks for the response. Also, except for the reference i quoted above and one or two papers that i could find(that were prohibitively mathematical), is there a source/reference that you know explains above steps with respect to aliasing and alias cancellation? Thanks $\endgroup$
    – user915783
    Sep 17 '14 at 18:36
  • $\begingroup$ There is a paper you can find online called " Time Aliasing Methods of Spectrum Estimation" -- it might help. $\endgroup$
    – John
    Sep 17 '14 at 21:01

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