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Complex Digital Signal Processing in Telecommunications

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**Search Introduction to Digital Filters**

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A filter is minimum phase if both the numerator and denominator of its
transfer function are
*minimum-phase polynomials*
in :

The case 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
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.

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/ for details.

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