IIR数字滤波器的MATLAB实现

论文总字数：12773字

摘 要

现如今通信系统飞速发展，许多信号分析都基于滤波器来进行,因为在信号被许多因素干扰，产生失真。这种情况下，就需要滤波器对信号进行处理。按照处理的信号种类，可分为模拟滤波器和数字滤波器。其中数字滤波器是通过数值运算来实现滤波的。而根据数字滤波器冲激响应函数的时域特性，数字滤波器又可以再被细分为无限长冲激响应数字滤波器（IIR数字滤波器）和有限长冲激响应数字滤波器（FIR数字滤波器）两种。其中IIR滤波器实现的阶次较低，能够保留模拟滤波器的一些优点的同时还具有存储单元占用较少并且效率和精度比较高的特点，因此在这个领域MATLAB得到重视。由于MATLAB丰富的信号处理工具箱和强大的过程计算功能，可以对IIR数字滤波器的设计参数进行调整而大大加快设计进程，减少许多工作量。

本文依据模拟滤波器的设计方法，从而对IIR数字滤波器进行设计，并且运用MATLAB编程对IIR数字滤波器进仿真。本文主要研究两种设计方法，脉冲响应不变法和双线性变换法设计IIR数字滤波器。前者是对模拟滤波器的冲激响应进行等间隔取样，目的在于让数字滤波器的单位脉冲序列正好等于模拟滤波器冲激响应的取样值，在经过特定的变换得到数字滤波器，这种方法使得数字滤波器保留了模拟滤波器的线性相位，但不可避免的产生混叠效应。双线性变换法使S平面和Z平面建立逐一对应的单值关系，从而不会产生混叠效应。

关键词：MATLAB；数字滤波器；无限长冲击（IIR）数字滤波器；脉冲响应不变法；双线性变换法。

MATLAB implementation of IIR digital filter

Abstract

Nowadays rapid development of communication system for many signal analysis based on filter, because in the signal will inevitably be often mixed with all kinds of interference and noise. Has a stable, flexible, and the advantages of high precision, no impedance matching problem of digital filter is implemented by numerical computation filtering, so that they can special filtering functions of analog filter is unable to realize. And infinite impulse response (IIR) digital filter and finite impulse response (FIR) digital filter two kinds of digital filter is based on time domain characteristics of digital filter impulse response function. Implementation of IIR filter, and have a low order to preserve some of the advantages of analog filter at the same time also has a storage unit take up less and high efficiency and accuracy, so widely used. As a result of the rich signal processing toolbox of MATLAB computing functions and powerful process, can be adjusted to the design of IIR digital filter parameters and greatly accelerate the process of design, reduce a lot of work.

IIR digital filter design method is proposed in this paper according to the design method of analog filter, and in the MATLAB environment of IIR digital filter design and simulation. This paper mainly studies two kinds of design method of impulse response is not political reform design of IIR digital filter and bilinear transform IIR digital filter design. The former is the impulse response of analog filter, such as sampling interval, the purpose is to let the unit pulse sequence of the digital filter is exactly equal to the sampling value of the analog filter impulse response, after a specific transformation to get digital filter, this method makes the linear phase digital filter to retain the analog filter, but inevitably produce aliasing effect. Bilinear transformation method and does not produce the aliasing effect, because it makes the S plane and Z plane of one-to-one correspondence relationship, eliminate the multiple value transformation.

Keyword：MATLAB;Digital filter；IIR digital filter；Impulse response is not political reform; Bilinear transformation method.

目录

摘要 ...................................................................................I

Abstract ..............................................................................II

1. 引言

1.1 课题研究的背景及意义

1.1.1数字信号处理概述 .........................................................1

1.1.2 MATLAB简介 ..............................................................1

1.2 本文主要研究内容 ...............................................................1

1. 滤波器的基本介绍

2.1 滤波器的定义 ...................................................................2

2.2 滤波器的分类 ...................................................................2

2.2.1 数字滤波器的原理与设计........................................................2

1. IIR数字滤波器的设计与实现

3.1 IIR数字滤波器设计方法 ..........................................................4

3.2 IIR数字滤波器的设计过程 ........................................................4

3.2.1 利用脉冲不变法对IIR数字滤波器进行设计 ...................................5

3.2.2 利用双线性Z变换法对IIR数字滤波器设计 ...................................6

第四章 MATLAB实现IIR数字滤波器

4.1 IIR数字滤波器的典型设计方法及仿真 .............................................9

4.2 IIR数字滤波器的直接设计方法及 .................................................12

总结 ..................................................................................13

谢辞 ..................................................................................14

参考文献 ..............................................................................15

附录 ..................................................................................16

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