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Higher-Order TIIR Filters

We have

\begin{eqnarray*}
H_{\rm FIR}(z)&=& H_{\rm IIR}(z) - z^{-N} H'_{\rm IIR}(z)\\
&=& \frac{B(z)-z^{-N}B'(z)}{A(z)}
\end{eqnarray*}

The corresponding difference equation is

\begin{eqnarray*}
y[n]&=& -\sum_{k=1}^P a_k y[n-k] +\sum_{\ell=0}^P
b_\ell x[n-\ell]\\ &&\nonumber\quad {}-\sum_{m=0}^{P-1}
b'_m x[n-m-(N+1)]
\end{eqnarray*}

Since the denominators of $ H_{\rm IIR}(z)$ and $ H'_{\rm IIR}(z)$ are the same, the dynamics (poles) can be shared:

\epsfbox{eps/sharedDynamics.eps}


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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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