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Complexity Notes

Note that there is a pole-zero cancellation in the TIIR transfer function

$\displaystyle H(z) = h_0 \frac{1- p^{N+1} z^{-(N+1)}}{1- p z^{-1}} = h_0 +h_0 p z^{-1} + \cdots+h_0 p^{N}z^{-N}
$

Basic Idea: Since the overall TIIR filter is FIR(N), alternate between two instances of each unstable one-pole, starting each new one from the zero state $ N$ samples before it is actually used. (Apparently first suggested by T. Fam at Asilomar-'87 for the case of distinct poles.)


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``Horn Modeling'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2019-02-05 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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