小波包分解树结点与信号子空间频带的对应关系及其应用

小波包变换的Mallat分解算法可以把较宽的信号频带划分成相等带宽且互不重叠的窄频带，但由于信号子空间频带的频率大小并非按照分解树结点（node）编号的大小顺序排列，各个结点重构信号的频率范围不易判定. 本文通过分析小波包变换的Mallat分解算法与分解滤波器的关系，设定频带编号与结点编号间进行二进制转化的运算规则，得到了小波包分解树结点与信号子空间频带的对应关系，然后通过模拟信号进行了验证. 结果表明，本文给出的小波包信号子空间频带的排列规则是正确的. 

Corresponding relationships between nodes of decomposition tree of wavelet packet and frequency bands of signal subspace

Mallat decomposition algorithm of wavelet packet transform can divide broader band into narrower ones with equal bandwidth and no overlapping each other. However, order by size of frequency within signal subspace is not in accordance with that of node label of decomposition tree. Therefore, it is not easy to determine frequency range of reconstructed signal from each node. In this paper, by analyzing the relationship between Mallat decomposition algorithm of wavelet packet transform and decomposition filter and setting operation rule of binary conversion of band labels into node labels, we find the corresponding relationships between nodes and frequency bands of signal subspace. Then, the conclusion is verified by analog signals. Also, it shows that the arranged rule of bands of signal subspace summarized in the paper is correct.