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Example

Desired Pole Radius

Pole radius $ R_k$ and $ t_{60}$ are related by

$\displaystyle R_k ^{t_{60}(\omega_k)/T} = 0.001
$

The ideal loss filter $ G(z)$ therefore satisfies

$\displaystyle \left\vert G(\omega)\right\vert^{t_{60}(\omega)/T} = 0.001
$

The desired delay-line filters are therefore

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

$ \Rightarrow$

$\displaystyle \left\vert G_i(e^{j\omega T})\right\vert^{\frac{t_{60}(\omega)}{M_iT}} = 0.001.
$

or

$\displaystyle \zbox{20 \log_{10}\left\vert G_i(e^{j\omega T})\right\vert = -60 \frac{M_i T}{t_{60}(\omega)}.}
$

Now use invfreqz or stmcb, etc., in Matlab to design low-order filters $ G_i(z)$ for each delay line.


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Download Reverb.pdf
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Download Reverb_4up.pdf

``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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