M带双正交多小波的平衡

Balance for M-Band Biorthogonal Multiwavelet

将平衡多小波的概念引入到M带r重双正交多小波系统,给出了相应的平衡条件,建立了M带r重双正交多尺度函数的若干等价关系,并基于这些等价关系给出构造双正交平衡多尺度函数和多小波的算法.算法在处理离散的多项式信号时,信号既能被低通滤波器保持,又能被高通滤波器取消,同时算法还保持了双正交多小波的对称性,这一点在信号处理方面具有很好的应用价值.

The notion of balancing is introduced to M-band biorthogonal muhiwavelet system,the corresponding balanced conditions are presented, and some equivalent propositions of balanced multiscale functions are established. Based on these propositions, algorithms for constructing balanced multiscale function and multiwavelets are proposed. If discrete polynomial signals are dealt with by the algorithm, the signals are preserved by the lowpass filter and canceled by the highpass filter, and the algorithm keeps symmetry of biorthogonal multiwavelet system. The numerical examples show the applied significance in signal processing.