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Duality of COLA and Nyquist Conditions

Let $ \hbox{\sc Cola}(N)$ denote constant overlap-add using hop size $ N$ . Then we have (by the Poisson summation formula Eq.$ \,$ (8.30))

\begin{eqnarray*}
w &\in& \hbox{\sc Nyquist}(N) \Leftrightarrow W \in \hbox{\sc Cola}(2\pi/N) \qquad \hbox{(FBS)} \\ [10pt]
w &\in& \hbox{\sc Cola}(R) \Leftrightarrow W \in \hbox{\sc Nyquist}(2\pi/R) \qquad \hbox{(OLA)}
\end{eqnarray*}



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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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