According to the infinite product formula of scaling function s Fourier transform,combined with the Fourier transform relation between a function and its Hilbert transform,the paper derived an condition on how two wavelet bases constructed from two conjugate quadrature filters can be pairs of wavelet bases,and proposed a method on how to construct the pairs of wavelet bases.

An algorithm of wavelet packet analyze based on conjugate quadrature filter proposed and is applied to images edge detection.

For compactly supported biorthogonal multiwavelet system with dilation factor α and multiplicity r,a general method to construct many new length-(L+1) biorthogonal conjugate filters(BCFs) from a length-L BCFs is given,and the approach of constructing higher-order matrix BCFs from lower-order ones is presented simultaneously.

The power complementary pair was derived from the perfect reconstruction condition of digital conjugate quadrature filter banks to retain pairwise power complementary property and the lossless property, which could decrease the aliasing error of the 0 frequency and the low frequency region.

Firstly,we use one dimensional parameter orthogonal wavelet filter to approach a double orthogonal wavelet filter.

An orthogonal wavelet filter design method based on the lattice structure of perfect reconstruction filter bank, is proposed in this paper.