三进小波尺度函数序列的特性及构造

Properties and Construction of Rank 3 Wavelet Scaling Sequences

为了克服二进小波的缺陷和拓宽小波的应用 ,研究了M进小波的多分辨分析和正交性条件 ,给出了一种构造正交三进小波尺度函数对应的滤波器系数的新方法 ,得出了M进小波尺度传递函数对应的有限冲激响应系数最少为MN(N为小波函数的消失矩或阶数 )个的结论 。

To overcome the disadvantages of the dyadic wavelet and extand the scope of wavelet applications, the multiresolution analysis and orthogonal condition of rank M wavelet are studied. A new method for constructing the filter coefficients corresponding to the rank 3 wavelet scaling function is presented. And the conclusion is drawn that the number of the FIR coefficients corresponding to the rank M wavelet scaling function is at least MN , where N is the vanishing moment of the vavelet function. Rank M wavelet has potential advantages over the traditional wavelets in image compression.\;