The Analysis and Design of Nearly-Orthogonal Symmetric Wavelet Filter Banks

The design and analysis of nearly-orthogonal symmetric wavelet filter banks has been studied. Methods for analyzing the correlation of the nearly-orthogonal filter banks are proposed. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter, minimize the deviation of the filter satisfying the orthogonal condition, and a nearly orthogonal filter bank can be obtained. Since multiple zeros are imposed, a scaling function may be generated from the minimized filter. The integer translates of the wavelet and the scaling functions are nearly orthogonal. The integer translates of the wavelet at different scale are completely orthogonal. We will construct a perfect reconstructed semi-orthogonal filter bank. Detailed analysis of correlation of the nearlyorthogonal filter banks are given in this paper.