The Algebra Method Of Constructing Spline Wavelet

Wavelet analysis is a prosperous research field in contemporary mathematics. The research of its theory and application is very important ,so the construction of wavelet bases is becoming more and more popular.The general methods constructing wavelet bases use FT and ZT (Fourier Transform and Z Transform), but they are not easy to be understood. In order to make clear of the construction wavelet bases, this paper uses the knowledge of function space and algebra, provides algebraic constructions of semi-orthogonal wavelet bases and biorthonormal wavelet, then summarize its rule. This construction methods make the choice of wavelet coefficients is satisfactory . Furthermore, a method to get the coefficients of Daubechies orthogonal wavelet is presented. It is based on the knowledge of original orthogonal wavelet and simplify the process. In a word, we present some simpler and more understandable algebraic construction of wavelet bases. These constructions will help people understand , apply and develop the knowledge of wavelets.Compared with Fourier Transform, we construct wavelet bases using only the relationship of function space and the knowledge of linear algebra. So the construction all of length-limit semi-orthogonal wavelets can be transformed to be linear algebraic problems. The same method also can be used to construct the corresponding wavelets function of lifting closing degree.