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Example: Polyphase Analysis of the STFT with 50% Overlap, Zero-Padding, and a Non-Rectangular Window

Figure: Polyphase representation of the STFT with a more general window and $ M/2$ hop size ($ 50$ % overlap).
\includegraphics[width=\twidth]{eps/polyNchanWinZPSTFT}

Figure 11.26 illustrates how a window and a hop size other than $ N$ can be introduced into the polyphase representation of the STFT. The constant-overlap-add of the window $ w(n)$ is implemented in the synthesis delay chain (which is technically the transpose of a tapped delay line). The downsampling factor and window must be selected together to give constant overlap-add, independent of the choice of polyphase matrices $ \bold{E}(z)$ and $ \bold{R}(z)$ (shown here as the $ \hbox{\sc DFT}$ and $ \hbox{\sc IDFT}$ ).


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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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