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Method

The FIR part is first extracted, and the (strictly proper) remainder is passed to residuez for expansion of the IIR part (into a sum of complex resonators). One must remember that, in this case, the impulse-response of the IIR part $ R(z)$ begins after the impulse-response of the FIR part $ F(z)$ has finished, i.e.,

$\displaystyle H(z) = F(z) + z^{-{N_f}}R(z)
$

where $ N_f$ is the length of the FIR part (order of $ F(z)$ plus 1).

See §6.8.8 for an example usage of residued (with a comparison to residuez).


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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
CCRMA