DocumentCode :
1544668
Title :
A new class of orthonormal symmetric wavelet bases using a complex allpass filter
Author :
Zhang, Xi ; Kato, Akira ; Yoshikawa, Toshinori
Author_Institution :
Dept. of Electr. Eng., Nagaoka Univ. of Technol., Niigata, Japan
Volume :
49
Issue :
11
fYear :
2001
fDate :
11/1/2001 12:00:00 AM
Firstpage :
2640
Lastpage :
2647
Abstract :
This paper considers the design of the whole sample symmetric (WSS) paraunitary filterbanks composed of a single complex allpass filter and gives a new class of real-valued orthonormal symmetric wavelet bases. First, the conditions that the complex allpass filter has to satisfy are derived from the symmetry and orthonormality conditions of wavelets, and its transfer function is given to satisfy these conditions. Second, the paraunitary filter banks are designed by using the derived transfer function from the viewpoints of the regularity and frequency selectivity. A new method for designing the proposed paraunitary filterbanks with a given degrees of flatness is presented. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez exchange algorithm. Therefore, the filter coefficients can be easily obtained by solving the eigenvalue problem, and the optimal solution is attained through a few iterations. Furthermore, both the maximally flat and minimax solutions are also included in the proposed method as two specific cases. The maximally flat filters have a closed-form solution without any iteration. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method
Keywords :
all-pass filters; channel bank filters; digital filters; discrete wavelet transforms; network synthesis; Remez exchange algorithm; WSS paraunitary filterbank design; closed-form solution; complex allpass filter; discrete wavelet transform; filter coefficients; frequency selectivity; generalized eigenvalue problem; maximally flat filters; minimax solution; optimal solution; orthonormal symmetric wavelet bases; orthonormality conditions; real-valued orthonormal symmetric wavelet bases; transfer function; whole sample symmetric filterbanks; Design methodology; Digital filters; Discrete wavelet transforms; Eigenvalues and eigenfunctions; Filter bank; Finite impulse response filter; Frequency; Nonlinear filters; Signal processing; Transfer functions;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.960410
Filename :
960410
Link To Document :
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