基于MATLAB的线性常系数差分方程求解.

数字信号处理课程设计

题目：基于MATLAB的线性常系数差分方程求解学院：

专业：

班级：

学号：

姓名：

指导教师：

目录

摘要 (1)

第一章背景 (3)

1.1 背景知识 (3)

1.2 《数字信号课程》特点 (3)

1.3 软件介绍 (4)

1.4 MATLAB及数字信号处理 (4)

第二章设计目的及要求 (6)

2.1 设计目的 (6)

2.2 课程设计的内容要求 (7)

2.2.1 设计要求 (7)

第三章设计任务 (8)

第四章设计原理 (9)

4.1 差分与差分方程 (9)

4.2 线性常系数差分方程 (14)

4.3 线性常系数差分方程的求解 (15)

第五章设计过程 (16)

5.1 用MATLAB求解差分方程 (16)

第六章设计代码及结果 (18)

6.1 MATLAB源程序 (18)

6.2 程序运行结果 (20)

6.3 比较结果总结 (24)

第七章收获与体会 (25)

致谢 (27)

参考文献 (28)

摘要

《数字信号处理》分析了数字信号处理课程的重要性及特点，为了帮助学生理解与掌握课程中的基本概念、基本原理、基本分析方法，提出了用MATLAB进行数字信号处理课程设计的思路，并阐述了课程设计的具体方法、步骤和内容。

MATLAB语言是一种广泛应用于工程计算及数值分析领域的新型高级语言，MATLAB功能强大、简单易学、编成效率高，深受广大科技工作者的喜爱，特别是MATLAB还具有信号分析工具箱，不需具备很强的编程能力，就可以很方便地进行语音信号分析、处理和设计。

线性常系数差分方程求解是数字信号处理课程中常出现的课题，也是现代科学中值得深入研究的一个课题

本文介绍了线性常系数差分方程的基本概念，论述了其求解方法，并用MATLAB具体实现了线性常系数差分方程的求解。

基于MATLAB的线性常系数差分方程求解主要是用MATLAB作为工具平台，设计中涉及到差分方程的递推求解以及用filter对系数向量的归一化等等。通过数字信号处理课程的理论知识的综合运用，从实践上初步实现对数字信号的处理。

关键字：MATLAB，线性常系数差分方程，数字信号处理。

Abstract

" Digital signal processing " analysis of digital signal processing course of the importance and features, in order to help the students to understand and grasp basic concepts, basic principles, basic analysis method, is put forward with the MATLAB for digital signal processing curriculum design, curriculum design and describes the specific methods, steps and content.

The MATLAB language is widely used in engineering calculation and the numerical analysis in the field of advanced language, MATLAB powerful, easy to learn, a high efficiency, by the vast number of scientific workers' favorite, especially the MATLAB also has a signal analysis toolbox, does not need to have very strong ability of programming, can be very convenient for the analysis of speech signal, processing and design.

Linear constant coefficient differential equation is a digital signal processing program that often appear in the topic, as well as modern science and worthy of in-depth study of a topic

This paper introduces the linear constant coefficient differential equation basic concept, discussed the solution method, and MATLAB the specific realization of linear constant coefficient difference equation.

MATLAB based on the linear constant coefficient difference equation MATLAB is mainly used as a tool platform, design relate to differential equation recursive solution and the use of filter on the coefficient vector is normalized and so on. Through the course of digital signal processing theory, the integrated use of knowledge, from the practice of preliminary implementation of digital signal processing.

Key words: MATLAB,Linear constant coefficient differential equation,Digital signal processing.