Filter Length Of 4 Compactly Supported Orthogonal Wavelet Bases Constructed

Wavelet analysis is one of the rapidly developed subject in these 20 years, and made great progress and achievements, and has been transformed into effective social productivity. Because of the uniqueness and huge social value of this science, has attracted a lot of scientists doing research and exploration.With the rapid progress of wavelet analysis domain, the wavelet basis plays irreplaceable fundamental role, the selection of wavelet basis decides the results of wavelet transformation. If the wavelet basis construction is convenient and feasible and has many good properties, it will promote the actual application. Different wavelet basis will get different eigenvalue after decomposition, so in order to choose proper wavelet according to specific issue, otherwise it is difficult to achieve satisfactory results. Thus construct wavelet basis becomes an important work in wavelet application.Wei Wenbin from Air force academy in radar impose a method to construct wavelet basis that adopt a filter in fixed length, introducing parameters in the filter to gets a series of distinguish and related wavelets which have compactly supported and orthogonality. but his study of the filter has certain limitation, this paper is based on this research to further study the structural characteristics of compactly supported orthogonal wavelet basis which the length of its filter is 4, the more generalized conditions are found in which wavelet basis still keeps compactly support and orthogonality after the parameter is added into the coefficient of the filter, and this paper also construct the example to verify the correctness of conclusion, so this paper in some extent deepens the constructing algorithm of wavelets which have compactly supported and orthogonality, promotes its convenience and maneuverability.