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Polynomials in the Delay

A more parametric approach is to formulate each filter coefficient $ h_\Delta(n)$ as a polynomial in the desired delay $ \Delta$ :

$\displaystyle h_\Delta(n) \isdefs \sum_{m=0}^M c_n(m)\Delta^m, \quad n=0,1,2,\ldots,N \protect$ (5.9)

Taking the z transform of this expression leads to the interesting and useful Farrow structure for variable FIR filters [135].


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-10-15 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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