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Choice of Delay Lengths

Mean Free Path

$\displaystyle {\overline d} = 4\frac{V}{S}\qquad\hbox{(mean free path)}

where $ V$ is the total volume of the room, and $ S$ is total surface area enclosing the room.

Regarding each delay line as a mean-free-path delay, the mean free path length, in samples, is the average delay-line length:

$\displaystyle \frac{{\overline d}}{cT} = \frac{1}{N} \sum_{i=1}^N M_i

where $ c$ = sound speed and $ T$ = sampling period.

This is only a lower bound because many reflections are diffuse in real rooms, especially at high frequencies (one plane-wave reflection scatters in many directions)

Mode Density Requirement

FDN order = sum of delay lengths:

$\displaystyle M \mathrel{\stackrel{\Delta}{=}}\sum_{i=1}^N M_i\qquad\hbox{(FDN order)}

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``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