Optimal Least-Squares Filters

In §B.2, we found that the optimal length FIR filter, in the least-squares sense, was obtained by simply matching the first terms of the desired impulse response. However, this was less than ideal for audio work due to the heavy ``Gibbs phenomenon'' in the frequency-domain response. We therefore prefer to formulate the filter-design problem in the frequency domain. This section describes various frequency-domain formulations for FIR digital filter design, including the least-squares case.

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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.