Title :
Wavelets generated by IIR filter banks
Author :
Herley, Cormac ; Vetterli, Martin
Author_Institution :
Dept. of Electr. Eng., Columbia Univ., New York, NY, USA
Abstract :
The relation between orthogonal finite impulse response filter banks and orthonormal bases of compactly supported wavelets has been established by Daubechies (1988). Building on this result, the authors use infinite impulse response (IIR) filter banks to construct more general orthonormal wavelet bases, which have infinite support, but rapid decay. They give a complete constructive method which gives all rational orthogonal two-channel filters banks. A family of wavelets is developed which have similar smoothness and moment properties to those of Daubechies. Wavelet bases are derived for the space of piecewise polynomial functions, which are alternatives to the Battle-Lemarie bases (Battle, 1987; Lemarie, 1988) and have the desirable property of being realizable. Relevant design exchanges are presented
Keywords :
digital filters; filtering and prediction theory; piecewise polynomial techniques; wavelet transforms; IIR filter banks; compactly supported wavelets; constructive method; design exchanges; infinite impulse response; moment properties; orthogonal finite impulse response filter banks; orthonormal bases; piecewise polynomial functions; rational orthogonal two-channel filters banks; smoothness; Buildings; Channel bank filters; Discrete wavelet transforms; Filter bank; Finite impulse response filter; IIR filters; Multiresolution analysis; Polynomials; Wavelet analysis; Wavelet domain;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1992. ICASSP-92., 1992 IEEE International Conference on
Conference_Location :
San Francisco, CA
Print_ISBN :
0-7803-0532-9
DOI :
10.1109/ICASSP.1992.226326
