The analysis of FIR biorthogonal wavelet filter banks with approxiamte orthogonality

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, then a nearly orthogonal filter bank can be obtained. Since multiple zeros are imposed, a scaling function may be generated from the minimized filter. The question is that what is the corresponding wavelet, since this nearly orthogonal filter bank is not perfect reconstructed. And besides, what is the degree of orthogonality of the wavelet bases. The way in this paper is to find a FIR complementary filter of the minimized filter and thus construct a perfect reconstructed biorthogonal 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.