Allpass Filter Design

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 [42,41]. Nonparametric methods, while suboptimal, can design very large-order allpass filters, and errors can usually be made arbitrarily small by increasing the order [100,70,1], [78, 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, [35,72]). As a result, perceptually weighted nonparametric methods can often outperform optimal parametric methods in terms of cost/performance. For a nonparametric method that can design very high-order allpass filters according to highly flexible criteria, see [1].