基于MATLAB的频谱分析及信号去噪仿真研究
摘 要
本课题为基于MATLAB的频谱分析及信号去噪仿真研究，是综合运用数字信号处理的理论知识，对含噪声的信号进行去噪处理，并对信号的时域和频域进行分析。通过理论推导得出相应结论，再利用 MATLAB 作为编程工具进行计算机实现。
本文主要围绕着信号的去噪进行研究，包括给定信号的去噪，以及信号的频谱分析。应用数字信号处理的相应理论，以MATLAB为实验工具，分别设计了IIR滤波器以及FIR滤波器对给定噪声信号进行去噪。在设计实现的过程中，使用窗函数法来设计FIR数字滤波器，用巴特沃斯设计IIR数字滤波器，并利用MATLAB 作为辅助工具完成设计中的计算与图形的绘制，与此同时也利用了均值滤波和中值滤波的方法对噪声信号进行处理，并分析了不同去噪方法所适用的信号类型。通过对给定信号的去噪仿真，对比不同去噪方式的去噪效果。
文中对不同去噪方法的去噪效果以及对不同信号适应什么样的去噪方法进行了详细的阐述，使人们今后在进行信号去噪时可以更有针对性的选择去噪方法。
关键词 ： 频域分析； 滤波器； 中值滤波；均值滤波
I
Spectrum Analysis and Signal Denoising
Based on the MATLAB
Abstract
The topic is spectrum analysis and signal denoising based on the MATLAB, it is comprehensive use of the knowledge of the digital signal processing, to denoise the signal containing noise, and analyze the signal in time domain and frequency domain. the The corresponding result get through theoretical derivation, then, using MATLAB as a programming tool for computer implementation.
This paper mainly focuses on the research of signal denoising, including the given signal denoising, as well as the signal spectrum analysis,the corresponding theoretical application of digital signal processing,taking MATLAB as experimental tools,designed IIR filter and FIR filter denoising for a given noise signals. To design FIR digital filter with window function method,design of IIR digital filter with Butterworth , drawing the result use of MATLAB as a tool to complete the calculation and graphic design,at the same time also used the method of mean filter and median filter to the noise signal,and analysis of the different types of signal for denoising method. By the denoising simulation for the given signal, comparing the different denoising methods denoising effect.
This topic were studied with the problem of signal denoising, denoising effect
analysis of different signal denoising method as well as the different signal to adapt to what kind of denoising method is further explained, So that people can be more targeted selection of denoising method in signal denoising in the future.
Key words: frequency-domain analysis; filter ; median filter; mean filter;
II
目 录
摘 要 ............................................................... I Abstract ............................................................ II 第1章 绪论 .......................................................... 1
1.1课题背景 ...................................................... 1 1.2 研究意义 ...................................................... 2 1.3 本文研究的主要内容 ............................................ 2 第2章 信号的频谱分析 ................................................. 4
2.1 频谱分析简介 .................................................. 4 2.2采样定理 ...................................................... 4 2.3 快速傅立叶变换 ................................................ 5 2.4 离散傅立叶变换 ................................................ 6 2.5频谱分析原理 .................................................. 6 2.6 信号的频谱分析 ................................................ 7 2.7 本章小结 ..................................................... 14 第3章 典型信号去噪方法 ............................................. 15
3.1 IIR和FIR滤波器的设计 ....................................... 15 3.2 典型信号的去噪对比 ........................................... 17
3.2.1 IIR低通滤波器去噪 ...................................... 17 3.2.2 FIR低通滤波器去噪 ..................................... 20 3.2.3 IIR与FIR滤波器处理结果的比较分析 ..................... 23 3.3 中值滤波与均值滤波 ........................................... 24
1