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


Fourier Theorems for the DTFT

This section states and proves selected Fourier theorems for the DTFT. A more complete list for the DFT case is given in [264].3.4Since this material was originally part of an appendix, it is relatively dry reading. Feel free to skip to the next chapter and refer back as desired when a theorem is invoked.

As introduced in §2.1 above, the Discrete-Time Fourier Transform (DTFT) may be defined as

$\displaystyle X(\omega) \isdef \sum_{n=-\infty}^\infty x(n) e^{-j\omega n}.$ (3.8)

We say that $ X$ is the spectrum of $ x$ .



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