Wavelet Theory And Its Application

As a new offset of mathematics,wavelet analysis is becoming a focus on some domain of science,it is internationaly recognized up to the minute tools for analysing time-frequency. Because of its " adaptive feature " and " mathematical microtelescope feature ", it is fondly delighted as tools for so many scientific workers.It plays an important role in the signal and imformation processing. Wavelet Transform is the core technology in JPEG2000.This paper aims at providing the kownledge of wavelet theory and its practical application. The main contributions are as follows:Firstly, the defects of Fourier Transform are discussed and the fundamental concept of Multi-resolution are illustrated.Secondly, several commonly-used wavelets and their construction methods is investigated, the basic priciple of Continuous Wavelet Transform and Discrete Hyper-wavelet Transform is introduced in details.Thirdly, introduced a key step in wavelet's application,which is how to construct the wavelet's filters. In this paper, some famous usual wavelets, mul-tiwavelets and multi-bank wavelets' filters are constructed, and some good properties are obtained. In addition, some application examples in many respects are demonstrated.Fourthly,implemention of Continuous Wavelet Transform and Discrete Hyper-wavelet Transform is investigated, and principle of wavelet application is analyzed, lots of implemention models in many respects are been given out,too.Fifthly, some relationships of multiwavelet and multi-bank wavelet's filters are stuied.