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FIR Transfer Function

The transfer function of an FIR filter is given by the z transform of its impulse response. This is true for any LTI filter, as discussed in Chapter 6. For FIR filters in particular, we have, from Eq.$ \,$ (5.6),

$\displaystyle H(z) \isdef \sum_{n=-\infty}^{\infty} h_n z^{-n} = \sum_{n=0}^M b_n z^{-n} \protect$ (6.8)

Thus, the transfer function of every length $ N=M+1$ FIR filter is an $ M$ th-order polynomial in $ z^{-1}$ .


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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