matlab实现线性卷积和循环卷积

编号：

数字信号处理

实训 (论文)说明书

题目：用matlab实现两信号的卷积

院（系）：应用科技学院

专业：电子信息工程

学生姓名：***

学号： ********** 指导教师：严素清童有为纪元法

2011 年 6 月29日

摘要

本文讲述的是运用matlab软件编写线性卷积和循环卷积，运行程序并得到正确结果，附上运行结果图让大家参照对比。

MATLAB是一款在数学类科技应用软件中特别是在数值计算方面首屈一指的软件，它可以进行矩阵运算、绘制函数和数据、实现算法、创建用户界面、连接其他编程语言的程序等，主要应用于工程计算、控制设计、信号处理与通讯、图像处理、信号检测、金融建模设计与分析等领域。而线性卷积和循环卷积在工程上的应用亦非常广泛，在Matlab软件处理下，实现任意两个序列的线性和循环卷积对于工程上的辅助是相当重要的。卷积关系最重要的一种情况，就是在信号与线性系统或数字信号处理中的卷积定理。利用该定理，可以将时间域或空间域中的卷积运算等价为频率域的相乘运算，从而利用FFT等快速算法，实现有效的计算，节省运算代价。

本文从线性卷积和循环的定义出发，分析其运算原理以及相关的公式、程序，着重介绍并分析了卷积的运算过程，让大家明白什么是卷积。程序运行之后得到正确的结果，将运行后正确的波形图图放在本次论文中让大家直观的做比较。

关键词：Matlab；线性卷积；循环卷积；波形图；正确

Abstract

This is about using matlab software linear convolution and cyclic convolution, operation procedure and get the right result, enclosed operation result diagram let everybody reference MATLAB is a type of technology in applications of mathematics, especially in numerical calculation of the leading software, which can be matrix calculation, and data mapping function, the realization of algorithms, creation of user interface, connected to other procedures, such as programming languages, the main application in engineering computing, control design, signal processing and communications, image processing, signal detection, financial modeling in areas such as design and analysis. And linear convolution in the application of engineering has a very wide range of software in Matlab, the realization of any two sequences of linear convolution support for projects is very important. Convolution relationship between the most important case, that is linear in the signal and digital signal processing system or the convolution theorem. Use of the theorem can be time-domain or space domain to the convolution operation in frequency domain equivalent of the multiplication operation, thus the use of FFT and other fast algorithms, the calculation of effective, cost-saving operation.

From linear convolution and circulation of the definition, analyzes its operation principle and relevant formula, procedures, and emphatically introduces and analyses the convolution operation process, let everyone know what convolution. After the program is running properly after operation, the results will be put on the right of the waveform Desmond tutu paper let everybody intuitive to compare.

Key words：Matlab；Linear convolution；Circular convolution；Sequence；Wave；Right

目录

引言 (1)

1 MATLAB软件简介 (1)

1.1 MATLAB的优势 (1)

1.2 MATLAB的组成 (3)

2 卷积分析 (3)

2.1 卷积的定义 (3)

2.2 线性卷积的运算 (4)

2.3 循环卷积的运算 (5)

3 MATLAB设计线性卷积 (5)

3.1 线性卷积的分析 (5)

3.2 线性卷积的设计流程图 (6)

3.3 线性卷积的MATLAB设计源程序 (6)

4 MATLAB设计循环卷积 (8)

4.1 循环卷积的分析 (8)

4.2 根据循环卷积分析设计流程图 (8)

4.3 根据循环卷积流程图设计matlab源代码 (10)

5 总结 (11)

谢辞 (12)

参考文献 (13)