Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Dual Views of the Short Time Fourier Transform (STFT)

In the overlap-add formulation of Chapter 8, we used a hopping window to extract time-limited signals to which we applied the DFT. Assuming for the moment that the hop size $ R=1$ (the ``sliding DFT''), we have

$\displaystyle \zbox {X_m(\omega_k) = \sum_{n=-\infty}^\infty [w(n-m) x(n)] e^{-j\omega_k n}.} \protect$ (10.1)

This is the usual definition of the Short-Time Fourier Transform (STFT) (§7.1). In this chapter, we will look at the STFT from two different points of view: the OverLap-Add (OLA) and Filter-Bank Summation (FBS) points of view. We will show that one is the Fourier dual of the other [9]. Next we will explore some implications of the filter-bank point of view and obtain some useful insights. Finally, some applications are considered.



Subsections
Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

[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
CCRMA