We consider the design of 6-channel tight frame symmetric wavelet with scaling factor M = 4. The lowpass filter is designed using either Grobner bases or truncated Taylor series methods. The bandpass and highpass filters are then designed using Grobner bases. The resulting filters have linear phase, smooth limit functions, and reduced redundancy. It was possible to obtain filterbanks with K₀ (zeros at z = 1 and z = ±j for the lowpass filter) up to 5 and Kmin (zeros at z = 1 for bandpass/highpass filters) of 1 or greater. The proposed filterbanks generate five wavelets and a scaling function with the underlying filters related as follows: H_5-i(z) = H_i(-z), i = 0... 5.

Date Published: 27 September 2011
PDF: 11 pages
Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381T (27 September 2011); doi: 10.1117/12.893059

Published in SPIE Proceedings Vol. 8138:
Wavelets and Sparsity XIV
Manos Papadakis; Dimitri Van De Ville; Vivek K. Goyal, Editor(s)