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COLA Examples

So far we've seen the following constant-overlap-add examples:

  • Rectangular window at 0% overlap (hop size $ R$ = window size $ M$ )
  • Bartlett window at 50% overlap ( $ R\approx M/2$ ) (Since normally $ M$ is odd, `` $ R\approx M/2$ '' means ``R=(M-1)/2,'' etc.)
  • Hamming window at 50% overlap ( $ R\approx M/2$ )
In addition, we can mention the following cases (referring to window types discussed in Chapter 3):
  • Rectangular window at 50% overlap ( $ R\approx M/2$ )
  • Hamming window at 75% overlap ($ R=M/4=25$ % hop size)
  • Any member of the Generalized Hamming family at 50% overlap
  • Any member of the Blackman family at 2/3 overlap (1/3 hop size); e.g., blackman(33,'periodic'), $ R=11$
  • Any member of the $ L$ -term Blackman-Harris family with $ R\approx M/L$ .
  • Any window with R=1 (``sliding FFT'')
Recall from §3.2.6, that many audio coders use the MLT sine window. The window is applied twice: once before the FFT (the ``analysis window'') and secondly after the inverse FFT prior to reconstruction by overlap-add (the so-called ``synthesis window''). Since the window is effectively squared, it functions as a Hann window for overlap-add purposes (a member of the Generalized Hamming family). As such, it can be used with 50% overlap. More generally, any positive COLA window can be split into an analysis and synthesis window pair by taking its square root.

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STFT of COLA Decomposition
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Overlap-Add Decomposition