小波分析及其在信号处理中的应用
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摘要
小波理论的形成是数学家、物理学家和工程师们多学科共同努力的结果，小波分析正在自然学科中不同寻常的流行着，已经成为当前最强有力的分析工具之一，而且还在继续蓬勃向前发展着。研究小波的新理论、新方法以及新应用具有重要的理论意义和实用价值。本文旨在进一步拓宽小波的应用范围，主要研究小波分析在信号检测、参数估计、特征提取等信号处理中的应用，并重点研究在通信信号领域中的应用。其主要内容可概括为以下几个方面：
基于传统的阈值去噪方法，在分析研究了它们的优缺点之后，本着改进滤波效果，提高去噪质量的目的，提出了一种改进方案。该改进方案克服了传统阈值去噪方法的缺陷，并适用于进一步的自适应滤波的需求，仿真试验证实了该改进方案的有效性和优越性。
Cramer-Rao下界是信号检测理论中的重要部分，它对参数估计有相当大的价值。本文在小波变换的基础上，推导出了相位是多项式的这种通信信号其相位系数的Cramer-Rao下界，并与以前其它方法得到的多项式相位信号系数的Cramer-Rao下界作比较，通过仿真试验及理论分析证实了小波变换对参数估计的实用价值。
特征提取是信号检测、模式识别等信号处理领域中至关重要的环节，本文基于信息论中互信息的概念，提出了一种识别通信信号的特征提取算法。该算法针对含参量的特征进行特征提取和特征选择，是原始特征中不含参数的特征提取算法的深入和完善。仿真结果表明这种基于最大互信息原则的最优化特征提取算法产生的新的特征使判决器具有很高的识别率。
The theory of the wavelet originates with mathematicians, physicists and engineers together,and now,the wavelet analysis is very popular in many fields of science as one of the most efficient tool to analysis or deal the problem, furthermore,it will still progress forward activitively in the future.To study the new theory,methods and applications of wavelets is of great theoretical significance and practical value.This paper aims to develop the new scopes of wavelet applications,chiefly studying the applications of the wavelet analysis in the signal processing,such as signal detection, parameters estimation and features extraction and especially dealing with the communication signals.The major works can be summarized as follows:After the analysis and study of the classical thresholding denoising methods, this paper presents a new thresholding function based on them,as their modified project, in order to improve the denoising effect .This modified project can overcome the shortcomings of the classical thresholding denoising methods in some extent ,moreover,it can be applied to the adaptive wavelet thresholding denoising algorithm,which is verified through a good many of simulation experiments.The Cramer-Rao lower bound theory is a very important part of the theory of signal detection and is of great value to parameters estimation. In this paper,based on the wavelet transform, we estimate the phase coefficients of a communications signal with a polynomial phase and the corresponding Cramer-Rao lower bounds are derived .Compared with other available algorithms,this kind of approach displays its much better efficiency and its even higher practical values via theoretical analysis and computer simulations.Features extraction is a very important link in some signal processing, signal detection,pattern recognition or classification and so on. Many class separability criteria.like distance criterion,divergence criterion and entropy criterion,are used for feature extraction .Using the concept of mutual information in the information theory, in this paper, a new feature extraction criterion and algorithm are proposed to solve the very kind probloms of parameterized ones,which is a further study of the non-parameterized ones. Simulstion results delicate that the new features produce a very high identication rate deriving from this algorithm based on the maximum mutual
information criterion.
基于传统的阈值去噪方法，在分析研究了它们的优缺点之后，本着改进滤波效果，提高去噪质量的目的，提出了一种改进方案。该改进方案克服了传统阈值去噪方法的缺陷，并适用于进一步的自适应滤波的需求，仿真试验证实了该改进方案的有效性和优越性。
Cramer-Rao下界是信号检测理论中的重要部分，它对参数估计有相当大的价值。本文在小波变换的基础上，推导出了相位是多项式的这种通信信号其相位系数的Cramer-Rao下界，并与以前其它方法得到的多项式相位信号系数的Cramer-Rao下界作比较，通过仿真试验及理论分析证实了小波变换对参数估计的实用价值。
特征提取是信号检测、模式识别等信号处理领域中至关重要的环节，本文基于信息论中互信息的概念，提出了一种识别通信信号的特征提取算法。该算法针对含参量的特征进行特征提取和特征选择，是原始特征中不含参数的特征提取算法的深入和完善。仿真结果表明这种基于最大互信息原则的最优化特征提取算法产生的新的特征使判决器具有很高的识别率。
The theory of the wavelet originates with mathematicians, physicists and engineers together,and now,the wavelet analysis is very popular in many fields of science as one of the most efficient tool to analysis or deal the problem, furthermore,it will still progress forward activitively in the future.To study the new theory,methods and applications of wavelets is of great theoretical significance and practical value.This paper aims to develop the new scopes of wavelet applications,chiefly studying the applications of the wavelet analysis in the signal processing,such as signal detection, parameters estimation and features extraction and especially dealing with the communication signals.The major works can be summarized as follows:After the analysis and study of the classical thresholding denoising methods, this paper presents a new thresholding function based on them,as their modified project, in order to improve the denoising effect .This modified project can overcome the shortcomings of the classical thresholding denoising methods in some extent ,moreover,it can be applied to the adaptive wavelet thresholding denoising algorithm,which is verified through a good many of simulation experiments.The Cramer-Rao lower bound theory is a very important part of the theory of signal detection and is of great value to parameters estimation. In this paper,based on the wavelet transform, we estimate the phase coefficients of a communications signal with a polynomial phase and the corresponding Cramer-Rao lower bounds are derived .Compared with other available algorithms,this kind of approach displays its much better efficiency and its even higher practical values via theoretical analysis and computer simulations.Features extraction is a very important link in some signal processing, signal detection,pattern recognition or classification and so on. Many class separability criteria.like distance criterion,divergence criterion and entropy criterion,are used for feature extraction .Using the concept of mutual information in the information theory, in this paper, a new feature extraction criterion and algorithm are proposed to solve the very kind probloms of parameterized ones,which is a further study of the non-parameterized ones. Simulstion results delicate that the new features produce a very high identication rate deriving from this algorithm based on the maximum mutual
information criterion.
引文
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