Results

Figure B.6 presents the frequency response of the optimal Chebyshev FIR filter corresponding to the window-method FIR filter shown in Fig.B.5. Note that the upper transition band ``blows up''. This is a well known failure mode in FIR filter design using the Remez exchange algorithm. It can be eliminated by narrowing the transition band, as shown in Fig.B.7. There is no error penalty in the transition region, so it is necessary that each one be ``sufficiently narrow'' to avoid this phenomenon.

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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.