FIR Filters

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

NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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FIR Filters

$\ FIXME: Consider adding a section here on the one-zero filter, as in the filter tutorial. Or scan it, finally.$\

$\ FIXME: Leverage Matlab here -- this is analysis$\

Figure B.1:The general, causal, finite-impulse-response (FIR)digital filter.
\

Figure B.1 depicts the general, causal, finite-impulse-response filter (FIR). The impulse response $h(n)$is obtained at the output when the input signal is the impulse signal $\. More formally, the impulse signal is defined by

\

If the $k$th tap is denoted $h_k$, then it is obvious from Fig. B.1that the impulse response signal is given by

\

In other words, the impulse response simply consists of the tap coefficients, prepended and appended by zeros.


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