信号奇异点的分步检测法

英文篇名：Hierarchical singular point detection based on wavelet transform
中文刊名：计算机工程与应用
英文刊名：Computer Engineering and Applications
作者：刘密歌 ; 李小斌
英文作者：LIU Mige ; LI Xiaobin ; Department of Mechanical and Electronic Engineering ; Xi’an University of Arts and Science ; Xidian University
中文关键词：信号的奇异性 ; 小波变换 ; 奇异点检测
英文关键词：singularity of signal ; wavelet transform ; singular point detection
出版日期：2012-05-21
机构：西安文理学院机械电子工程系;西安电子科技大学;
年：2013
期：12
出版单位：计算机工程与应用

摘要

针对两种常见的信号奇异点:脉冲型奇异点和阶跃型奇异点,证明信号的奇异点与信号小波变换的最值有关,如果适当选择小波基函数,那么信号的脉冲奇异点将对应于小波基函数的最值点,而信号的阶跃奇异点将对应于小波基函数的原函数的最值点。据此,设计了一个新的基于小波变换的信号奇异点分步检测法(Hierarchical Singular Point Detection based on Wavelet Transform,HSPDWT),该方法的特点是根据脉冲奇异点和阶跃奇异点的不同特征分两步从信号中提取奇异点。仿真及真实信号上的实验证明了HSPDWT的可行性和有效性。
For two major classes of signal singular points, the pulse singular point and the step singular point, it is showed that the maximum absolute value of real wavelet transform can be used to detect the singularity in signal. It is further showed that, by using the wavelet basis function chosen carefully, the pulse singular point in signal exactly corresponds to the maximum absolute value point of the real wavelet basis function, and the step singular point corresponds to the maximum absolute value point of the primitive function of the real wavelet basis function. As a result, a hierarchical singular point detection method is developed.An important characteristic of the method is that in the course of singular point detection the singular points are detected step by step according to their features. The experimental results on a number of artificial and real signals are very encouraging and show the method can indeed identify the singularity from signals successfully.

引文

[1]Mallat S,Hwang W L.Singularity detection and processing with wavelets[J].IEEE Transactions on Information Theory,1992,38:617-643.
    [2]Tu C L,Hwang W L,Ho J.Analysis of singularities from modulus maxima of complex wavelets[J].IEEE Transactions on Information Theory,2005,51:1049-1062.
    [3]张燕,吴云,刘永启,等.小波分析在地壳形变资料处理中的应用[J].地震学报,2004,26(S1):103-109.
    [4]李文光,刘晰戈.基于小波变换的血压信号特征提取方法研究[J].计算机仿真,2006,23(11):91-94.
    [5]Tsantis S,Dimitropoulos N,Ioannidou M,et al.Inter-scale wavelet analysis for speckle reduction in thyroid ultrasound images[J].Computerized Medical Imaging and Graphics,2007,31:117-127.
    [6]Hsung T,Lun D P.Application of singularity detection for the deblocking of JPEG decoded images[J].IEEE Transactions on Circuits and Systems-II:Analog and Digital Signal Processing,1998,45(5):640-644.
    [7]Hsung T,Lun D P,Siu W.Denoising by singularity detection[J].IEEE Transactions on Signal Processing,1999,47(11):3139-3144.
    [8]Mallat S.A wavelet tour of signal processing[M].2nd ed.USA:Academic Press,1999.
    [9]刘密歌,郭东道,李小斌.脉冲型奇异点的小波检测[J].电子测量技术,2009,32(4):17-19.
    [10]刘密歌,李小斌.阶跃型奇异点的小波检测[J].计算机仿真,2010,27(5):314-317.