一维离散小波变换在信号降噪中的应用—张凯剖析.doc

学士学位论文 一维离散小波变换在信号降噪中的应用 学院、 物理与电子信息学院 通信工程 研 究 方 向 学 生 姓 名 学 号 指导教师姓名 指导教师职称 2015年 月 日 摘要：本篇论文主要开展的是对一维离散小波变换在信号降噪中的应用研究。首先简单的叙述了小波变换，其中简要说明傅里叶变换和小波变换的定义，概述了多分辨率分析以及介绍了三种常用的小波函数；然后进一步介绍了一维离散小波降噪的原理和方法；再利用不同的小波基对含有相同噪声的信号进行小波分解，通过随机列举两个不同的小波基对含有相同噪声的不同信号进行去噪，通过MATLAB仿真，得出滤波后的信号，并且通过对滤波前与滤波后的信号进行直观比较与参数分析。仿真结果表明：对相同的噪声信号的去噪处理不同的小波基可以有不同的去噪效果。因此小波基的选取要结合信号特点、统计特性等来确定。 关键词 The application of one-dimensional discrete wavelet transform in signal denoising Zhangkai School of Physics and Electronic Information, Huaibei Normal University, 235000 Abstract:This article mainly carries out the study on application of one-dimensional discrete wavelet transform in signal de-noising. Firstly wavelet de-noising introduced simply, and also the background of wavelet transform and definition of continuous wavelet transform, orthogonal wavelet transform and discrete wavelet transform are illustrated; next it jumps to the discussion of the principle and method of wavelet de-noising which uses different wavelet based on the signal with the same noise by wavelet decomposition, and then, two different wavelet bases are listed at random which are used to de-noise different signals containing the same noise through MATLAB simulation, the filtered signals, and finally the signals are compared directly and parameters are analyzed before and after filtering. The simulation results show that:different wavelet bases which are applied to the same noisy signal de-noising can have different de-noising effects. Therefore, the selection of wavelet basis should be determined according to the signal characteristics, statistic characteristics and so on. Keywords:One-dimensional discrete wavelet transform；Signal de-noising；Wavelet；