测试系统中非平稳信号的时频优化小波包检测算法  

Measurement algorithm of nonstationary signal based on time and frequency optimization using wavelet packet transform

作　　者：边海龙[1,2] 陈光[2] 李林[1] 苏义脑[1] 

机构地区：[1]中国石油天然气总公司钻井技术研究院,北京100083 [2]电子科技大学自动化工程学院CAT实验室,成都610054

出　　处：《仪器仪表学报》2009年第3期498-502,共5页Chinese Journal of Scientific Instrument

基　　金：国家自然科学基金(90407007,60372001)资助项目

摘　　要：非平稳信号为测试系统所测试分析的主要目标之一。对于这些信号传统的检测方法(例如:傅里叶变换)不能起到有效的分析作用。小波包变换是非平稳信号分析的常用工具。Shannon小波函数是现有的单小波家族中唯一能够对信号频域进行严格划分的小波函数,但是由于其时域的非紧支性限制了其应用。本文通过对Shannon小波函数的时频联合优化,改善了其在非平稳信号检测过程中的性能;首先在时域上,改写其时域表达式,并保留其频域的紧支性,提升了其时域的紧支性;其次在频域上,提出了对Shannon小波函数频域滤波器的插值算法,改善其频域的滤波性能;再次,通过牛顿插值法给出了算法的快速实现;最后,做出了仿真实例。结果表明,通过本文的算法,改善了Shannon小波包变换的性能,使其成为测试系统关于非平稳信号检测的有效手段。Nonstationary signal is one of the most important targets analyzed in measurement field. Classic methods like the Fourier Transform （FT） could not be used effectively in this case. Wavelet Packet Transform （WPT） is one of the useful tools to analyze the nonstationary signals. Shannon wavelet function is the only one that can divide the frequency domain of the signal strictly in single wavelet function family. But the time waveform of Shannon wavelet is not compactly supported, so its application is limited. An algorithm is proposed in this paper, which optimizes the Shannon wavelet function both in time and frequency domains synchronously. Firstly, in time domain, by modifying the time expression of the function, the performance of the time filter is improved ; secondly, an interpolation algorithm in frequency domain is proposed to improve the frequency filtering characteristic ; then a fast computation implementation of the algorithm is given by applying the Newton iterative algorithm. Finally, numeric simulation is carried out. The result proves that the algorithm can improve the performance of the transform effectively and can be used as one of the powerful nonstationary signal test tools in the measurement system.

关 键 词：Shannon小波包变换 时域提升 频域插值 非平稳信号检测 

分 类 号：TP315[自动化与计算机技术—计算机软件与理论]