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 [278,277]. Nonparametric, methods, while suboptimal, can design very large-order allpass filters, and errors can usually be made arbitrarily small by increasing the order [563,372], [432, 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, [214,384]). As a result, perceptually weighted nonparametric methods can often outperform optimal parametric methods in terms of cost/performance [3].