So far we have looked at the design of linear phase filters. In this
case,
,
and
are all real. In some
applications, we need to specify both the *magnitude* and
*phase* of the frequency response. Examples include

- minimum phase filters [263],
- inverse filters (``deconvolution''),
- fractional delay filters [266],
- interpolation polyphase subfilters (Chapter 11)

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