Minimum-Phase Polynomials
A filter is minimum phase if both the numerator and denominator of its
transfer function are
minimum-phase polynomials
in :
The case![]()
![$ b_0=0$](http://www.dsprelated.com/josimages_new/filters/img1245.png)
![$ z=\infty$](http://www.dsprelated.com/josimages_new/filters/img985.png)
As usual, definitions for filters generalize to definitions for signals by simply treating the signal as an impulse response:
Note that every stable all-pole filter
is
minimum phase, because stability implies that
is minimum
phase, and there are ``no zeros'' (all are at
).
Thus, minimum phase is the only phase available to a stable all-pole
filter.
The contribution of minimum-phase zeros to the complex cepstrum was described in §8.8.
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Maximum Phase Filters
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Definition of Minimum Phase Filters