Conversion to Minimum Phase

As discussed in §11.7, any spectrum can be converted to minimum-phase form (without affecting the spectral magnitude) by computing its cepstrum and replacing any anticausal components with corresponding causal components. In other words, the anticausal part of the cepstrum, if any, is ``flipped'' about time zero so that it adds to the causal part. Doing this corresponds to reflecting non-minimum phase zeros (and any unstable poles) inside the unit circle in a manner that preserves spectral magnitude. The original spectral phase is then replaced by the unique minimum phase corresponding to the given spectral magnitude.

A matlab listing for computing a minimum-phase spectrum from the magnitude spectrum is given in §J.11.

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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/ for details.