Causal FIR Filters

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Causal FIR Filters

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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 © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Causal FIR Filters

From Eq. (B.2), we that the impulse response $h(n)$ is alwayszero for $n<0$. Any filter having a zero impulse response prior to time $0$ is said to be causal. Thus, a tapped delay line such as that depicted in Fig. B.1 can only implement causal FIR filters. In software, however, we may easily implement non-causal filters as well based simply on the definition ofconvolution. However, noncausal filters are never precisely physical, of course, since events are causal in the real world (disregarding certain effects in quantum mechanics).

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