Wavelet Analysis And Its Application To Signal Processing

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 mutualinformation criterion.