Creating Minimum Phase Filters

and Signals

Minimum-phase filter design often requires creating a minimum-phase
desired frequency response
(usually starting from a real
amplitude response
). As is clear from
§12.2, any filter transfer function can be made
minimum-phase, in principle, by completely factoring and
``reflecting'' all zeros for which inside the
unit circle, *i.e.*, replacing by . However, factoring a
polynomial this large can be impractical. An approximate
``non-parametric'' method is based on the property of the
*complex cepstrum* (see §8.4)
that each minimum-phase zero in the spectrum gives rise to a causal
exponential in the cepstrum, while each non-minimum-phase zero
corresponds to an anti-causal exponential in the cepstrum
[60]. Therefore, by computing the cepstrum and
converting anti-causal exponentials to causal exponentials, the
corresponding spectrum is converted to minimum-phase form.

A matlab function `mps.m` which carries out this method is
listed in §H.11.^{13.3} It works well for *smooth* desired frequency response
curves. Specifically, the inverse DFT of the log magnitude frequency
response should not be longer than the number of samples in the
frequency response (no ``time aliasing'').

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