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Dual of Constant Overlap-Add

In this section, we will derive the Fourier dual of the Constant OverLap-Add (COLA) condition for STFT analysis windows (discussed in §7.1). Recall that for perfect reconstruction using a hop-size of $ R$ samples, the window must be $ \hbox{\sc Cola}(R)$ . We will find that the equivalent frequency-domain condition is that the window transform must have spectral zeros at all frequencies which are a nonzero multiple of $ 2\pi/R$ . Following established nomenclature for filter banks, we will say that such a window transform is $ \hbox{\sc Nyquist}(2\pi/R)$ .



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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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