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The Reverberation Problem

Consider the requirements for acoustically simulating a concert hall or other listening space. Suppose we only need the response at one or more discrete listening points in space (``ears'') due to one or more discrete point sources of acoustic energy.

First, as discussed in §2.2, the direct signal propagating from a sound source to a listener's ear can be simulated using a single delay line in series with an attenuation scaling or lowpass filter. Second, each sound ray arriving at the listening point via one or more reflections can be simulated using a delay-line and some scale factor (or filter). Two rays create a feedforward comb filter, like the one in Fig.2.9 on page [*]. More generally, a tapped delay line (Fig.2.19) can simulate many reflections. Each tap brings out one echo at the appropriate delay and gain, and each tap can be independently filtered to simulate air absorption and lossy reflections. In principle, tapped delay lines can accurately simulate any reverberant environment, because reverberation really does consist of many paths of acoustic propagation from each source to each listening point. As we will see, the only limitations of a tapped delay line are (1) it is expensive computationally relative to other techniques, (2) it handles only one ``point to point'' transfer function, i.e., from one point-source to one ear,4.1 and (3) it should be changed when the source, listener, or anything in the room moves.

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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University