Biorthogonal Wavelet Construction Using Homotopy Method

The biorthogonal wavelets families are used widely because they have compact support, complete symmetry and linear phase. According to Bézout's theorem, the biorthogonal wavelets available now are only some particular examples of total solutions. The quantity of solutions is decided jointly by the scaling function vanishing moment N and dual vanishing moment Ñ. The relationship of N, Ñ and solutions' quantity is discussed in detail. According to the constraint conditions which the compact biorthogonal wavelets satisfy, a number of biorthogonal wavelets are constructed in which the global convergent homotopy method is used for different N and Ñ. The filter coefficients and plots of scaling function, dual scaling function, wavelet function and dual wavelet function are given.