M带离散时间子波变换

M-BAND DISCRETE TIME WAVELET TRANSFORM

二带连续时间子波变换可由无限级树形正交镜像滤波器(QMF)组产生,类似地,二带离散时间子波变换可表示为有限级树形QMF组。该文对二带离散时间子波变换进行了推广,给出了M带离散时间于波变换,并研究了M带离散时间子波变换与M带仿酉滤波器组之间的关系。结果表明,在L级M带树形滤波器组中,如果每级滤波器组是仿酉滤波器组,则该树形滤波器组所产生的离散时间子波基是正交基。

Two-band continuous time wavelets can be obtained from infinite-level binary tree-structured QMF banks. Similarly, two-band discrete time wavelet transform can be represented as a finite-level binary tree-structured QMF banks. In this paper, two-band discrete time wavelet transforms are generalized to M-band discrete time wavelet transforms. The relationship between M-band discrete time wavelet transforms and M-band paraunitary filter banks is also investigated. It is shown that if the filter banks on each level are paraunitary, the wavelet basis generated by this tree is orthonormal.