小波分解和高次小波差分的奇异点

摘要

A transform matrix B[n×n] for decomposing the sampled signal F[n]into Harr Wavelets series coefficients C[n] is presented，where n is the exponent of 2.As the inverse transform matrix B-1=BT,the wavelet transform matrix method is then quite convenient for decomposing C=B.F and reconstructing F=BT.C.If we first let C[k]=0,where k from 1 to n/2,then define the high-frequency wavelet difference C1[k]=C[k]-C[k-1],the peculiar changing point for the sampled signal F[n] will be presented.Some examples are illustrated.%提出小波变换矩阵B[n×n]，它可将数字采样数列F[n]分解为Haar小波级数的系数C[n]，其中n是2的整数次幂，小波变换逆矩阵B-1=BT，所以小波变换矩阵的方法能十分方便地进行小波分解C=B.F和小波重构F=BT.C。如令某些C[k]=0,其中k从1到n/2，然后令高次小波差分为C1[k]=C[k]-C[k-1]，它能为原函数F[n]指出它的奇异变化点，文中作了图示举例。