DocumentCode :
1334225
Title :
Constrained least square design of FIR filters without specified transition bands
Author :
Selesnick, Ivan W. ; Lang, Markus ; Burrus, C. Sidney
Author_Institution :
Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
Volume :
44
Issue :
8
fYear :
1996
fDate :
8/1/1996 12:00:00 AM
Firstpage :
1879
Lastpage :
1892
Abstract :
This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR filters and gives the best L2 filter and a continuum of Chebyshev filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs´ phenomenon without resorting to windowing or `smoothing out´ the discontinuity of the ideal lowpass filter
Keywords :
Chebyshev filters; FIR filters; convergence of numerical methods; delay circuits; digital filters; filtering theory; frequency response; least squares approximations; low-pass filters; Chebyshev filters; FIR filters; Kuhn-Tucker conditions; L2 filter; Lagrange multipliers; constrained least square design; cut-off frequency; filter design; frequency response; ideal lowpass filter; input signals; integral square error criterion; linear-phase FIR filters; minimum-phase FIR filters; multiple exchange algorithm; peak constrained lowpass FIR filters; rapidly converging algorithm; transition bands; Algorithm design and analysis; Chebyshev approximation; Cutoff frequency; Design methodology; Finite impulse response filter; Frequency response; Lagrangian functions; Least squares methods; Robustness; Smoothing methods;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.533710
Filename :
533710
Link To Document :
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