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Summary of Trade-Offs

Window-method filter:

$ (+)$
Filter length can be thousands of taps
$ (-)$
Stopband ``droops'' (rolls off) -- not $ L^\infty$ optimal
$ (-)$
Passband edge tuned slightly too low
Optimal Remez-Exchange filter:
$ (+)$
Stopband is ideal, equiripple
$ (+)$
Transition region close to half that of the window method
$ (+)$
Pass-band is ideal, equiripple
$ (+)$
Time-domain impulses from passband ripple are small
$ (-)$
Design time orders of magnitude larger than that for window method
$ (-)$
Fails to converge for filters much longer than 256 taps (Need to increase working precision to get longer filters)


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``The Window Method for FIR Digital Filter Design}'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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