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Causal (Periodic) Signals

A signal $ x\in{\bf C}^N$ may be defined as causal when $ x(n)=0$ for all ``negative-time'' samples (e.g., for $ n=-1,-2,\dots,-N/2$ when $ N$ is even). Thus, the signal $ x=[1,2,3,0,0]\in{\bf R}^5$ is causal while $ x=[1,2,3,4,0]$ is not. For causal signals, zero-padding is equivalent to simply appending zeros to the original signal. For example,

$\displaystyle \hbox{\sc ZeroPad}_{10}([1,2,3,0,0]) = [1,2,3,0,0,0,0,0,0,0].
$

Therefore, when we simply append zeros to the end of signal, we call it causal zero padding.


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``Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition'', by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8.
Copyright © 2014-04-21 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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