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Damping Filter Design

The damping filter $ G_i(z)$ associated with the delay line of length $ M_i$ in the FDN can be written in principle as

$\displaystyle G_i(z) = G_T^{M_i}(z) L_i(z)
$

where $ G_T(z)$ is the lowpass filter corresponding to one sample of wave propagation through air, and $ L_i(z)$ is a lowpass corresponding to absorbing/scattering boundary reflections along the (hypothetical) $ i$ th propagation path.

Define

\begin{eqnarray*}
t_{60}(\omega)&=& \mbox{desired reverberation time at frequency $\omega$}\\ [10pt]
p_k &=& e^{j\omega_kT} = \mbox{$k$th pole of the lossless prototype}
\end{eqnarray*}

We can introduce frequency-independent damping with the (conformal map) substitution

$\displaystyle z^{-1}\leftarrow g\,z^{-1}
$


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``Artificial Reverberation and Spatialization'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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