Tight frame 6-band symmetric wavelets with limited redundancy
Farras Abdelnour · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
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: H5-i(z) = Hi(-z), i = 0... 5.