Realization of Complex Wavelet Packet Transform with Perfect Translation Invariance

(1)证明了完全平移不变复离散小波变换(PTI-CDWT)不能直接推广到小波包变换。实现了两种具有多分辨率分析结构的近似平移不变复小波包变换(ATI-CWPT)。第一种是代换型复小波包变换，第二种是相位补偿复小波包变换。(3)将这两种ATI-CWPTs应用于分析线性系统的输入输出关系。这是分析线性系统时变频率特性的基本工具。(4)将本文提出的ATI-CWPTS应用于探地雷达在凿岩和埋地管道定位中对异常声波信号的分析。我们开发的变换的有效性在工业应用中得到了证明。

The results of this study are summarized as follows :(1) We showed that the perfect translation invariant Complex Discrete Wavelet Transform(PTI-CDWT) cannot be directly extended to the wavelet packet transform. But, it can be realized without multi-resolution analytical structure.(2) We realized two approximate translation invariant Complex Wavelet Packet Transforms(ATI-CWPTs) with multi-resolution analytical structure. The first is called Substitution-type Complex Wavelet Packet Transform, and the second is the Phase-Compensated Complex Wavelet Packet Transform.(3) We applied these two ATI-CWPTs to analysis of the input-output relation of linear systems. This is a basic tool for analyzing time-variant frequency characteristics of linear systems.(4) We applied our proposed ATI-CWPTs to analysis of extraordinary sound signals in rock drilling and location of buried pipes by using Ground-Penetrating Radar. The effectiveness of our developed transforms was demonstrated in industry applications.