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First-Order Delay-Filter Design

Jot used first-order loss filters for each delay line:

$\displaystyle H_i(z) = g_i \frac{1-a_i}{1-a_iz^{-1}}
$

Design formulas:

\begin{eqnarray*}
g_i &=& 10^{-3 M_i T / t_{60}(0)}\\
a_i &=& \frac{\mbox{ln}(10)}{4}\log_{10}(g_i)\left(1-\frac{1}{\alpha^2}\right)
\end{eqnarray*}

where

$\displaystyle \alpha \mathrel{\stackrel{\Delta}{=}}\frac{t_{60}(\pi/T)}{t_{60}(0)}
$


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Download Reverb.pdf
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Download Reverb_4up.pdf

``Artificial Reverberation and Spatialization'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2007-09-19 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