基于MATLAB的卷积演示系统

目录

摘要 (2)

ABSTRACT (3)

第一章背景 (4)

1.1MATLAB的优点 (4)

1.2MATLAB的组成 (5)

第二章设计原理及分析 (7)

2.1卷积的定义 (7)

2.2线性卷积的运算 (7)

2.3循环卷积的运算 (8)

第三章设计内容与分析 (9)

3.1设计内容 (9)

3.2线性卷积的分析 (9)

3.3循环卷积的分析 (9)

第四章实验代码及结果 (10)

4.1线性卷积的MATLAB设计源程序 (10)

4.2循环卷积的MATLAB设计源程序 (11)

4.3分析两类卷积关系 (13)

4.4动态演示基于重叠相加法的长序列快速卷积 (13)

4.5用MATLAB设计一个卷积演示界面 (16)

第五章收获与体会 (19)

致谢 (20)

参考文献 (21)

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

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