A Family Of Biorthogonal Wavelets In L～2(Z)

Butterworth filters are related to some biorthogonal wavelets, called But-terworth wavelets. Those wavelets have nice properties which include symmetry, the interpolation and vanishing moments. In this paper, a general concept for biorthogonal wavelet bases in l~2(Z) is introduced and an easily checked sufficient condition is given, by which the Butterworth wavelets are derived; then a family of biorthogonal wavelets are constructed, which have all properties of the Butterworth wavelets; Moreover, our wavelets have the shortest possible supports.This thesis is organized as follows: In the first Chapter, some necessary notations, the background and the main results of this paper are given; in the second part, a general concept for biorthogonal wavelet bases in l~2(Z) is introduced and an easily checked sufficient condition is shown, by which the Butterworth wavelets are derived; In the third part, a class of biorthogonal wavelets are constructed, which have symmetry, interpolation property and vanishing moments of lower order; In chapter 4, we extend the results of last chapter to the general case with vanishing moments of order 2r; Moreover, our wavelets have the shortest possible supports.