基于MATLAB的IIR数字滤波器的设计与仿真

摘要1

ABSTRACT2

前言3

第1章滤波器的基本概念4

1.1 滤波器的定义4

1.2 滤波器的发展4

1.3 滤波器的分类5

第2章滤波器的原理与设计7

2.1 模拟滤波器的原理与设计7

2.2 数字滤波器的原理与设计8

第3章 IIR数字滤波器的设计10

3.1 IIR数字滤波器简介10

3.2 IIR数字滤波器的主要技术指标10

3.3 IIR数字滤波器的设计过程12

3.3.1用脉冲相应不变法设计IIR数字滤波器13

3.3.2双线性变换法设计IIR数字滤波器16

第4章 IIR数字滤波器的实现20

4.1 matlab简介20

4.1.1 matlab的概况20

4.1.2 matlab的语言特点20

4.1.3 matlab的功能22

4.2 利用模拟原型进行IIR数字滤波器的设计和仿真23

4.2.1巴特沃斯(Butterworth)和椭圆数字低通滤波器的设计24

4.2.2切比雪夫（Chebyshev）数字滤波器的设计30

4.3 IIR数字滤波器的直接设计法34

第5章 IIR数字滤波器的综合设计和仿真40

5.1数字低通滤波器设计实例与仿真40

5.2数字带通滤波器设计实例与仿真42

结论45

致谢46

参考文献47

毕业设计小结48

摘要

在现代通信系统中，由于信号中经常混有各种噪声和干扰，所以很多信号分析都是基于滤波器而进行的，而数字滤波器是通过数值运算实现滤波，具有处理精度高、稳定、灵活、不存在阻抗匹配问题等优点，可以实现模拟滤波器无法实现的特殊滤波功能。数字滤波器根据其冲激响应函数的时域特性，可分为两种，即无限长冲激响应(IIR)数字滤波器和有限长冲激响应(FIR)数字滤波器。实现IIR滤波器的阶次较低，所用的存储单元较少，效率高，精度高，而且能够保留一些模拟滤波器的优良特性，因此应用很广。Matlab软件以矩阵运算为基础，把计算、可视化及程序设计有机融合到交互式工作环境中，并且为数字滤波的研究和应用提供了一个直观、高效、便捷的利器。尤其是Matlab中的信号处理工具箱使各个领域的研究人员可以直观方便地进行科学研究与工程应用。

本文根据模拟滤波器的设计原理，提出了IIR数字滤波器的设计方法，并在MATLAB环境下实现了IIR数字滤波器的设计和仿真。其主要内容概括为：首先对滤波器的原理和设计进行了介绍；接着描述了IIR数字滤波器的基本概念，其中包括系统的描述、系统的传递函数、系统的模型；接着简单介绍MATLAB，并对数字滤波器在MATLAB环境下如何实现进行了介绍；重点描述了IIR数字滤波器的设计过程，最后对IIR滤波器进行仿真。

关键词：MATLAB，IIR数字滤波器，模拟滤波器

ABSTRACT

In modern communication system,because the signal is often mixed with various noise and interference, so a lot of signal analysis are based on the filter and the digital filter, and through numerical arithmetic to realize filtering, has high processing precision, stable, flexible, there is no problem of impedancematching and other advantages, can realize analog filter can achieve special filtering function.Digital filter based on the impulse response function in the time domain characteristics, can be divided into two types, namely, infinite impulse response (IIR) digital filters and finite impulse response (FIR) digital filter.Realization of IIR filter order is relatively low, the storage unit is less, high efficiency, high precision, and can retain some analog filter of excellent properties, so the application is very wide.Matlab software for matrix computation based on the calculation, visualization, and the program design of the organic integration of the interactive environment, and digital filtering for applications in research and provides an intuitive, efficient, convenient tool.Especially the Matlab signal processing toolbox to various fields of research personnel can undertake scientific research and engineering application.In this paper, according to the analog filter design theory, puts forward the design of IIR digital filter method, and MATLAB environment in the realization of IIR digital filter design and simulation.Its main content is wraparound for: first on the filter principle and design are introduced; then described the IIR basic concepts of digital filter, which includes system is described, the transfer function of the system, system model; then a brief introduction of the MATLAB, and the digital filters in the MATLAB environment how to realization are introduced; focus on the description of IIR digital filter design process, the last of the IIR filter simulation.

KEY WORDS:MATLAB, IIRdigital filter,Dimulation filt