Multiband Delay-Filter Design

In §3.7.5, we derived first-order FDN delay-line filters which can independently set the reverberation time at dc and at half the sampling rate. However, perceptual studies indicate that reverberation time should be independently adjustable in at least three frequency bands [217]. To provide this degree of control (and more), one can implement a multiband delay-line filter using a general-purpose filter bank [370,500]. The output, say, of each delay line is split into bands, where is recommended, and then, from Eq.(3.6), the gain in the th band for a length delay-line can be set to

to produce the desired decay-time in that band, where denotes the desired 60-dB decay time in samples. Faust implementations of FDN reverberator along these lines are described in §3.7.9 below.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.