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

The design and analysis of one-dimensional (1D) 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 then a nearly orthogonal filter bank can be obtained. The way in this paper is to find a FIR complementary filter of the minimized filter and thus construct a perfect reconstructed bi-orthogonal filter bank. Then a corresponding wavelet filter bank can be generated and correlation analysis can also be conducted. The integer translates of the wavelet at the same scale is also nearly-orthogonal, the disadvantage is that orthogonal degree of the integer translates of the wavelet at different scale is lower than that of the semi-orthogonal filter bank.