The Compactly Supported Four-bank Orthonormal Wavelet Bases With Linear Phase

The general construction of compactly supported 4-bank orthonormal wavelets with linear phase are mainly studied in this thesis.In the begin-ning,wavelet analysis theory and its application history are introduced. The 2-bank orthonormal wavelets theory is sketched, the basic concept of multi-bank orthonormal wavelets and their nature are summarized, and the concept of the minimum matrix of multi-band wavelets transforms is put forward.The paper focuses on the compactly supported 4-bank orthonormal wavelets with linear phase,the existing theoretical achievements are summarized system-atically. Then another two general kinds of such wavelets are studied, with the structure of filters given and the images depicted correspondingly based on the specific examples with the length of 4,8,12,16,20. The research shows that the orthonormal wavelets studied in this thesis include current "graceful wavelets", and the vanishing moment increase by two orders with the same filter length, thus they have superior functions.