Polyphase View of the Weighted-Overlap-Add STFT

International Standard Book Number — Click for https://mathworld.wolfram.com/ISBN.html

Search JOS Website

JOS Home Page

JOS Online Publications

Index of terms in JOS Website

Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Perfect Reconstruction Filter Banks

Polyphase View of the Overlap-Add STFT

Paraunitary Filter Banks

The Short Time Fourier Transform (STFT) computes the spectrum (DFT) of successive time frames of a signal. — Click for https://ccrma.stanford.edu/~jos/sasp/Short_Time_Fourier_Transform.html

A filter in the audio signal processing context is any operation that accepts a signal as an input and produces a signal as an output. Most practical audio filters are linear and time invariant, in which case they can be characterized by their impulse response or their frequency response. — Click for https://ccrma.stanford.edu/~jos/filters/What_Filter.html

Search JOS Website

JOS Home Page

JOS Online Publications

Index of terms in JOS Website

Index: Spectral Audio Signal Processing

Spectral Audio Signal Processing

Perfect Reconstruction Filter Banks

Polyphase View of the Overlap-Add STFT

Paraunitary Filter Banks

Example: Polyphase Analysis of the Weighted Overlap Add Case: 50% Overlap, Zero-Padding, and a Non-Rectangular Window

We may convert the previous example to a weighted overlap-add (WOLA) (§8.6) filter bank by replacing each by $\sqrt{w(m)}$ and introducing these gains also between the $\hbox{\sc IDFT}$ and upsamplers, as shown in Fig.11.27.

**Figure 11.27:** Polyphase representation of STFT using *Weighted OverLap Add (WOLA)*.
$\includegraphics[width=\twidth]{eps/polyNchanWinZPWOLA}$

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

``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

Example: Polyphase Analysis of the Weighted Overlap Add Case: 50% Overlap, Zero-Padding, and a Non-Rectangular Window

``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