Minimum Phase Means Fastest Decay

The previous example is an instance of the following general result:

That is, the signal energy in the first samples of the minimum-phase case is at least as large as any other causal signal having the same magnitude spectrum. (See [60] for a proof outline.) Thus, minimum-phase signals are maximally concentrated toward time 0 when compared against all causal signals having the same magnitude spectrum. As a result of this property, minimum-phase signals are sometimes called minimum-delay signals.

---

Order a Hardcopy of Introduction to Digital Filters

Previous: Example
Next: Minimum-Phase/Allpass Decomposition

---

written by 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/ for details.