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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].
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