**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW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 analysisFigure B.1 depicts the general, causal,

finite-impulse-response filter(FIR). Theimpulse responseis obtained at the output when the input signal is theimpulse signal. More formally, the impulse signal is defined by

If the th tap is denoted , then it is obvious from Fig. B.1that the impulse response

signalis given by

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

Subsections