## Minimum Phase Filter Design

Above we used the Hilbert transform to find the imaginary part of an
analytic signal from its real part. A closely related application of
the Hilbert transform is contructing a *minimum phase* frequency
response from an amplitude response.

Let denote a desired complex, minimum-phase frequency response,

*cepstrum*. It is shown in §E.9 below that a frequency response is minimum phase if and only if the corresponding cepstrum is causal [187, Ch. 10], [247, Ch. 11].

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