A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

Introduction of C Programming for DSP Applications

**Search Introduction to Digital Filters**

**Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?**

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 (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.

Comments

No comments yet for this page