Example

It is easy to classify completely all first-order FIR filters:

where we have normalized to 1 for simplicity. We have a single zero at . If , the filter is minimum phase. If , it is maximum phase. Note that the minimum-phase case is the one in which the impulse response decays instead of grows. It can be shown that this is a general property of minimum-phase sequences, as elaborated in the next section.

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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.