Title :
Nearly symmetric orthogonal wavelets with non-integer DC group delay
Author :
Selesnick, Ivan W. ; Odegard, Jan E. ; Burrus, C. Sidney
Author_Institution :
Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
Abstract :
This paper investigates the design of Coiflet-like nearly symmetric compactly supported orthogonal wavelets. The group delay is used as the main vehicle by which near symmetry is achieved. By requiring a specified degree of flatness of the group delay at ω=0 (equivalent to appropriate moment conditions), near symmetry is achieved. The way in which the group delay approximates a constant is a traditional measure of symmetry in filter design. Grobner bases are used to obtain the solutions to the defining nonlinear equations. It is found that the DC group delay that maximizes the group delay flatness at ω=0 is irrational, and for a length 10 orthogonal wavelet with three vanishing moments, the solution is presented
Keywords :
delays; filtering theory; nonlinear equations; signal processing; wavelet transforms; Grobner bases; filter design; group delay flatness; moment conditions; nearly symmetric orthogonal wavelets; noninteger DC group delay; nonlinear equations; orthogonal wavelet; signal analysis; vanishing moments; Finite impulse response filter; Frequency response; Nonlinear equations; Polynomials; Propagation delay; Transfer functions; Vehicles;
Conference_Titel :
Digital Signal Processing Workshop Proceedings, 1996., IEEE
Conference_Location :
Loen
Print_ISBN :
0-7803-3629-1
DOI :
10.1109/DSPWS.1996.555554