NDLI: A Remez exchange algorithm for orthonormal wavelets

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A Remez exchange algorithm for orthonormal wavelets

Content Provider	IEEE Xplore Digital Library
Author	Rioul, O. Duhamel, P.
Copyright Year	1992
Abstract	Compactly supported orthonormal wavelets are obtained from two-band paraunitary FIR filter bank solutions, with the additional "flatness" constraint that the low-pass filter should have K zeroes at half the sampling frequency. This constraint is set to obtain "regular" wavelets. However, it is somewhat in contradiction with the usual requirement for good frequency selectivity, since it is well known that maximally flat filters (yielding Daubechies wavelets) have poor frequency selectivity. An efficient procedure for designing maximally frequency selective filter banks under a given flatness constraint is described in this paper. Classical Remez exchange algorithms, based on the alternation theorem, can no longer be used in this case. Linear programming techniques are capable of setting up constraints of this type, but require high memory storage and computation time. First, a variation of the alternation theorem adapted to this new situation is derived. Then, a modified Remez exchange algorithm for the design of "wavelet" filters is derived in the spirit of the Parks-McClellan algorithm. The efficiency of the algorithm is greatly improved as compared to linear programming techniques, and optimum filters are generally obtained after 3 or 4 iterations. A MATLAB listing is provided.<>
Sponsorship	IEEE Circuits and Systems Society
Starting Page	550
Ending Page	560
Page Count	11
File Size	1042677
File Format	PDF
ISSN	10577130
Volume Number	41
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-08-01
Publisher Place	U.S.A.
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Finite impulse response filter Filter bank Low pass filters Frequency Linear programming Sampling methods Algorithm design and analysis Nonlinear filters MATLAB Band pass filters
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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