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FIR impulse response

The impulse response $ h(n)$ is obtained at the output when the input signal is the impulse signal $ \delta = [1,0,0,0,\ldots]$5.6). If the $ k$ th tap is denoted $ b_k$ , then it is obvious from Fig.5.5 that the impulse response signal is given by

$\displaystyle h(n)\isdef \left\{\begin{array}{ll} 0, & n<0 \\ [5pt] b_n, & 0\leq n\leq M \\ [5pt] 0, & n> M \\ \end{array} \right. \protect$ (6.6)

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


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2015-01-15 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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