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Embedded SystemsFPGAElectronics

Spectral Audio Signal Processing
    The Filter Bank Summation (FBS) Interpretation of the Short Time Fourier Transform (STFT)
       Duality of COLA and Nyquist Conditions

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Duality of COLA and Nyquist Conditions

Let $ \hbox{\sc Cola}(N)$ denote constant overlap-add using hop size $ N$. Then we have (by the Poisson summation formula Eq.$ \,$(7.4))

\begin{eqnarray*} w &\in& \hbox{\sc Nyquist}(N) \Leftrightarrow W \in \hbox{\sc ... ...trightarrow W \in \hbox{\sc Nyquist}(2\pi/R) \qquad \hbox{(OLA)} \end{eqnarray*}


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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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