【作者】 吕健；

【导师】 张承慧；

【作者基本信息】 山东大学 ， 控制理论与控制工程， 2008， 硕士

【摘要】 小波分析是在傅立叶分析基础上发展而来的新的时频分析工具,具备良好的时频局部化性质和多分辨率特性,在信号处理领域中得到广泛的应用。本论文对小波变换在信号滤波中的应用进行了研究。信号在采集、转换和传输过程中,由于受到设备、环境及人为因素的影响,使信号不可避免地受到噪声干扰。因此,如何去除信号中的噪声,得到感兴趣的信息是信号处理过程中的一项关键技术。根据小波变换的性质和噪声的统计特性,Donoho提出了小波阈值滤波方法,通过选择合适的阈值和阈值函数,对含噪信号的小波系数进行阈值化处理,可有效地去除噪声。本文研究了基于小波阈值的信号滤波问题,在阈值选取上,依据信号与噪声的小波系数在多尺度上的变化规律的不同,提出一种改进的阈值的选取方法,数值实验结果表明了该算法的有效性和可行性。针对传统的硬阈值函数和软阈值函数存在的缺陷,即硬阈值函数的不连续性,软阈值函数存在恒定偏差,提出了一种新的阈值函数,有效地克服了硬阈值函数和软阈值函数的缺点。实验结果表明,改进后的方法可获得更好的滤波效果。总之,本文所提出的新的阈值滤波方法获得了很好的结果,具有很好的稳定性和可靠性。更多还原

【Abstract】 Wavelet analysis developed from Fourier analysis is a new time-frequency analysis tool which has favorable time-frequency localized and multi-resolution properties. Wavelet analysis has been widely applied in signal processing field and other fields. In this paper, a fast signal reconstruction algorithm and a signal de-noising algorithm from its wavelet transform modulus maxima are presented.In the process of signal collection, transform and transmission, the signal often mix noise ineluctably because the equipments, environments and even human errors. De-noising with the purpose of extracting desired information has been a crucial technique in signal processing. Based on the properties of wavelet transform and the statistical characteristics of noise, Donoho presented the threshold de-noising in wavelet transform domain. By selecting appropriate threshold and threshold function, the noise can be suppressed.According to the different characters of Wavelet coefficients of signal and noise, a new threshold selection method is put forward. The experimental results show that this method is efficient and practical. But there are discontinuity of hard-threshold function and biased estimation of soft-threshold function. In this paper, a new threshold function which overcomes the inherent disadvantages of hard-threshold and soft-threshold is proposed. Experiments show that the improved method has better performance of de-noising than the traditional methods.In short, the new thresholding algorithm can reach the expected outcome and has good stability and reliability.更多还原