Design of approximate Hilbert transform pair of wavelets with exact symmetry

Abstract

This paper presents a new technique for designing pairs of filter banks whose corresponding wavelet function are approximate Hilbert transform of each other. The filters have exact linear phase which yields biorthogonal wavelets with exact symmetry. The technique is based on matching the frequency response of a given odd-length filter bank with an even-length filter bank. The class of EBFB (Even-length Bernstein Filter Bank) is utilized in the matching design. The EBFB has perfect reconstruction and vanishing moments properties structurally imposed and this simplifies the design process. The design is achieved through a non-iterative least squares method.