COLA Examples

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Convolving with Long Signals

Overlap-Add Decomposition

STFT of COLA Decomposition

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Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Convolving with Long Signals

Overlap-Add Decomposition

STFT of COLA Decomposition

COLA Examples

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

Rectangular window at 0% overlap (hop size = window size )
Bartlett window at 50% overlap ( $R\approx M/2$ ) (Since normally 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 ( % 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'),
Any member of the -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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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

COLA Examples

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1. Copyright © 2022-02-28 by Julius O. Smith III Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University