On Some Problems In The Construction Of Wavelet

Wavelet Analysis is a rapid development area in the modern mathematics. The produce and application are very important. Wavelet theory is the momentous break- through of the traditional Fourier transform. It begot a big attention of the many international science organization and subject field. It was been the current advanced subject. The development was very fast. It became appropriate character model of the sound,picture and signal. It especially fit disposal signal and picture with break in a short time. So it has a very abroad application.Based on deep research to the statuses of the wavelet theory at home and abroad. We do some research on the wavelet tight frame, multivariate multiple wavelet packet, symmetric interpolation wavelet, and continuous wavelet transform.Firstly, we introduce the concept of wavelet tight frame, and we study the constr- uction of bivariate 4-band wavelet tight frame. We give explicit constructing formula of bivariate 4-band wavelet tight frame. We derive the decomposition and reconstruc- tion formulas.Secondly, the definition of the biorthogonal quarternary multiwavelet packet is given and a procedure for constructing a class of biorthogonal quarternary multiwave- let packets is presented.Then, an algorithm for constructing 4-dimentional symmetric interpolation wav- elets are presented by an arbitrary quarternary orthogonal wavelets.In the end, a method of constructing trivariate continuous wavelet transform from 1-dimentional continuous wavelet transform is presented.