Tight frame 6-band symmetric wavelets with limited redundancy

Farras Abdelnour

doi:10.1117/12.893059

27 September 2011 Tight frame 6-band symmetric wavelets with limited redundancy

Farras Abdelnour

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81381T (2011) https://doi.org/10.1117/12.893059
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

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.

Citation Download Citation

Farras Abdelnour "Tight frame 6-band symmetric wavelets with limited redundancy", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81381T (27 September 2011); https://doi.org/10.1117/12.893059

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