Remez Exchange Algorithm

• The Remez multiple exchange algorithm works by moving the frequency samples each iteration to points of maximum error (on a denser grid).

• Remez iterations could be added to our formulation as well.

• The Remez multiple exchange algorithm (function firpm [formerly remez] in the Matlab Signal Processing Toolbox) is normally faster than a linear programming formulation, which can be regarded as a single exchange method cite[p. 140]RabinerAndGold.

• Another reason for the speed of remez is that it solves the following equations non-iteratively for the filter exhibiting the desired error alternation over the current set of extremal frequencies:

where is the weighted ripple amplitude at frequency . ( is an arbitrary ripple weighting function.) Note that the desire frequency response amplitude is also arbitrary at each frequency sample.

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Subsections

• Convergence of Remez Exchange

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Order a Hardcopy of Spectral Audio Signal Processing

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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.