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A filter is minimum phase if both the numerator and denominator of its
transfer function are
is excluded because the polynomial cannot be minimum
phase in that case, because then it would have a zero at
unless all its coefficients were zero.
As usual, definitions for filters generalize to definitions
for signals by simply treating the signal as an impulse
Note that every stable all-pole filter
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
The contribution of minimum-phase zeros to the complex cepstrum
was described in §8.8.
Previous: Definition of Minimum Phase FiltersNext: Maximum Phase Filters
About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA)
, teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/