基于Blackman窗函数插值的小波模极大值去噪算法

发布时间：2018-01-30 19:42

本文关键词： 信号去噪小波模极大值小波系数重构信号 Blackman窗函数　出处：《河南理工大学》2014年硕士论文　论文类型：学位论文

【摘要】：信号去噪算法的研究一直是信号处理领域的难点和热点,长期以来人们常用傅里叶变换分析处理信号,而且取得了较好的效果。然而傅里叶变换是一种全域的整体变换,只能显示一个域内的信号特性,对于分析非平稳信号有很大的局限性。小波变换是继傅里叶变换迅猛发展起来的一种分析非平稳信号的强有力工具,具有在时频域内同时表征信号局部化特性和多分辨分析的能力,不但在信号处理领域有极好的发展前景,而且与科学界其他领域相互融合、相互渗透形成一种新生力量。本文主要研究了利用小波模极大值重构小波系数实现信号重构的算法,在分析了模极大值直接重构算法和交替投影算法之后,总结了两种经典算法存在的优缺点,发现模极大值直接重构算法虽然简单快捷,但重构后的信号信息不完整,有较大失真;而交替投影算法虽然能达到很高的重构精度,但计算量太大,运算速度太慢,实用性不强。如何找到一种由信号的模极大值重构信号的合理有效、方便快捷的算法,就是本文要解决的问题。考虑到Blackman窗函数有主瓣宽且幅值大,旁瓣宽度小以及衰减速度快的特性,本文以Blackman窗函数作为插值函数,并在此基础上,构造了一种基于Blackman窗函数插值的小波模极大值去噪算法,该算法利用插值技术填补了各尺度上那些不是模极大值点的值,从而得到重构信号。最后采用blocks和bumps信号从重构精度、信噪比增益和运算时间上对本文构造的算法与两种经典算法进行了仿真比较,结果表明Blackman窗函数插值的去噪算法有较好的去噪效果,信号信息完整,计算量小,且失真小,收敛速度快,实用性较强。
[Abstract]:The research of signal denoising algorithm has been a difficult and hot spot in the field of signal processing. For a long time, people often use Fourier transform to analyze and process signals. But Fourier transform is a global transform, which can only show the signal characteristics in one domain. Wavelet transform is a powerful tool for analyzing non-stationary signals after Fourier transform developed rapidly. It has the ability of simultaneously characterizing signal localization and multi-resolution analysis in time-frequency domain. It not only has an excellent prospect in the field of signal processing, but also merges with other scientific fields. Mutual penetration forms a new force. This paper mainly studies the algorithm of signal reconstruction using wavelet modulus maximum reconstruction coefficients, after analyzing the modulus maximum direct reconstruction algorithm and alternating projection algorithm. The advantages and disadvantages of the two classical algorithms are summarized. It is found that the modulus maximum direct reconstruction algorithm is simple and fast, but the reconstructed signal information is incomplete and has large distortion. Although the alternating projection algorithm can achieve a high reconstruction accuracy, but the calculation is too large, the operation speed is too slow, the practicability is not strong. How to find a signal reconstruction signal from the modulus maximum reasonable and effective. The convenient and fast algorithm is the problem to be solved in this paper, considering that the Blackman window function has the characteristics of large amplitude and width of the main lobe, small width of the sidelobe and fast attenuation speed. In this paper, the Blackman window function is used as the interpolation function, and on this basis, a wavelet modulus maximum denoising algorithm based on the Blackman window function interpolation is constructed. The algorithm makes use of interpolation technique to fill up the values which are not modulus maximum points on each scale, and obtains the reconstructed signal. Finally, the blocks and bumps signals are used to reconstruct the precision. Compared with two classical algorithms in SNR gain and computation time, the results show that the denoising algorithm based on Blackman window function interpolation has better denoising effect. The signal information is complete, the computation is small, the distortion is small, the convergence speed is fast, and the practicability is strong.
【学位授予单位】：河南理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.4

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