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Allpass Filters

In general, (finite-order) allpass filters can be written as

$\displaystyle H(z) = e^{j\phi} z^{-K} \frac{\tilde{A}(z)}{A(z)}
$

where

\begin{eqnarray*}
A(z) &=& 1 + a_1 z^{-1}+ a_2 z^{-2} + \cdots + a_N z^{-N}\\
\...
...-1} z^{-1}+ \cdots + \overline{a}_1 z^{-(N-1)} + \cdots + z^{-N}
\end{eqnarray*}

The polynomial $ \tilde{A}(z)$ can be obtained by reversing the order of the coefficients in $ A(z)$ and conjugating them.



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``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA