Dispersion Filter Design

A pure dispersion filter is an ideal 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 [280,279]. Nonparametric, methods, while suboptimal, can design very large-order allpass filters, and errors can usually be made arbitrarily small by increasing the order [568,377], [437, 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, [216,389]). As a result, perceptually weighted nonparametric methods can often outperform optimal parametric methods in terms of cost/performance [2].

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written by 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.