3-band symmetric bi-orthogonal filter banks with compact support and their applications in signal processing

Abstract

Multi-band wavelets are newly emerging branch in wavelet family and could have better properties than dyadic wavelets in terms of symmetry, orthogonality, compact support and smoothness. The purpose of this paper is to present a new method for constructing the filter banks of 3-band symmetric bi-orthogonal wavelet using a scaling function of linear spline function. To construct such 3-band wavelet with desirable properties, a set of linear algebra equations can be listed according to the requirements of the bi-orthogonal multi-resolution analysis. And these equations are then solved to obtain the filter coefficients. The properties of the filters and the multi-resolution analysis (MRA) in signal processing are discussed. Experiments show that the 3-band filter banks could be potentially better in signal processing than dyadic wavelets.