小波分析对非稳信号的消噪.doc

小波分析对非平稳信号的消噪 摘要 小波分析是近十几年来应用数学和工程科学中一个迅速发展的研究领域，是由Fourier分析发展起来的一个新的数学方法，它既包含了丰富的数学理论，又是工程应用中强有力的方法和工具。它通过引入可变的尺度因子和平移因子，巧妙地解决了时频局部化的矛盾，弥补了Fourier分析的不足，是一种有效的时频分析方法。小波分析理论以其自身良好的时频特性在图像、信号去噪领域受到了越来越多的关注，开辟了非线性方法去噪的先河。 本文针对小波阈值去噪法进行了研究和探讨，主要包括：小波阈值去噪的基本理论，基本问题选取包括小波基、阈值、阈值函数，基于信号去噪的基本原理以及传统阈值函数，随后给出小波阈值函数的改进方案，它克服了传统阈值函数的缺陷，并通过仿真实验验证本文阈值函数去噪法的去噪效果。 此外，本文介绍了小波变换的基本思想和优点及多分辨率分析的过程, 并在MA TLAB 下利用小波变换工具箱, 编写程序实现信号去噪处理。充分显示了小波变换在处理非平稳信号中的优势。 关键词　小波分析； 非平稳信号； 噪声； 阈值函数 Wavelet analysis of non-stationary signal de-noising Abstract Wavelet analysis is applied mathematics and engineering science in last decade a rapid development in the field of study, is developed by Fourier analysis, a new mathematical method which contains abundant mathematical theory, is a powerful method in engineering application and tools. It by introducing a variable scale factor and shift factor, skillfully handle the relationship between the time-frequency localization, make up for the deficiency of the Fourier analysis, is a kind of effective method of time-frequency analysis. Wavelet analysis theory to its good time-frequency features in the field of image denoising, signal has been more and more attention, has opened up a nonlinear method of denoising. Wavelet thresholding de-noising method are researched and studied in this paper，including the basic theory of wavelet thresholding de-noising, the selecting of thewavelet basis, thresholding value and thresholding function. Base on the basic theoriesof signal de-noising and traditional thresholding function, Then an improvedthresholding function is proposed. This method overcomes the defects of the traditionalhresholding function. Were introduced in this paper the basic ideas and advantages of wavelet transform and multiresolution analysis process, and use wavelet transform under MA TLAB toolbox, write a program to realize signal de-noising processing. Fully shows the advantages of wavelet transform in non-stationary signal processing. Keywords T