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Dispersion Filter Design

A pure dispersion filter is ideal an allpass filter. That is, it has a gain of 1 at all frequencies and only delays a signal in a frequency-dependent manner.

There is a fairly large literature thread on the topic of allpass filter design. Generally, they fall into two main categories: parametric and nonparametric methods. Parametric methods can produce allpass filters with optimal group-delay characteristics [256,255]. Nonparametric, methods, while suboptimal, can design very large-order allpass filters, and errors can usually be made arbitrarily small by increasing the order [528,345], [404, pp. 60,172]. In music applications, it is usually the case that the ``optimality'' criterion is unknown because it depends on aspects of sound perception (see, for example, [197,357]). As a result, perceptually weighted nonparametric methods can often outperform optimal parametric methods in terms of cost/performance.


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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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