基于MATLAB的数字滤波器优化设计

论文编号:JD218      字数:13768,页数:40   

摘  要

数字滤波器是数字信号处理中最重要的组成部分之一。在许多科学技术领域中，广泛使用滤波器对信号进行处理。数字滤波器可以分为两类，即有限冲激响应数字滤波器(FIR)和无限冲激响应数字滤波器(IIR)。本文就分别对这两类数字滤波器的设计和实现来进行分析研究。
在FIR滤波器的设计过程中主要探讨了两个问题，其一是FIR线性相位滤波器的特点及相关公式推导；其二是用窗函数设计FIR滤波器,重点介绍了基于等波纹切比雪夫逼近准则实现了FIR数字滤波器的优化设计并通过MATLAB的仿真实现。
在IIR滤波器的设计过程中，将设计步骤分为三步，即模拟滤波器原型设计，模拟-数字滤波器变换，滤波器频带变换。着重介绍了频域直接设计法和优化设计法。在这两类滤波器的整个设计过程都是按照理论分析、编程设计、具体实现的步骤来进行的。

关键词：数字滤波器；有限冲激响应；无限冲激响应；优化设计算法；MATLAB
        

 Abstract

Digital filter is one of the most important parts of digital signal processing. In many fields of science and technology, it is widely used for signal processing. Digital filter can be divided as the Finite Impulse Response digital filter (FIR) and the Infinite Impulse Response digital filter (IIR).The paper aims at respective study in the design and realization of these two kinds of digital filters.
Two major points are discussed about the design of FIR filters: the characteristics of FIR linear phase filter and the reasoning of related formulas: the other is about the design of the FIR filters by means of window functions. Introduce with emphasis based on and so on ripple Chebychev approached the criterion to implement the FIR filters optimized design and through the MATLAB simulation implementation.
The design of IIR filters can be achieved through three steps: the design of prototype of analog low-pass filter, analog-to-digital filter conversion and the conversion of filter frequency band. Introduce the frequency range direct design law and the optimized design law emphatically. The design of FIR and IIR follows the procedures of theoretical analysis, programming design and concrete realization.
Key words：Digital Filter, FIR, IIR, optimization design algorithm, MATLAB

目  录

第一章  前言..................................................................1
1.1  数字滤波器的发展概况.....................................................1
1.2  MATLAB软件介绍 ..........................................................2
第二章  数字滤波器............................................................4
2.1  数字滤波器的设计与实现 ..................................................4
2.2  数字滤波器的分类 ........................................................4
2.3  数字滤波器的设计要求和方法 ..............................................5
2.3.1  幅频特性 ..............................................................5
2.3.2  相频特性 ..............................................................6
2.4  数字滤波器设计方法概述 ..................................................9
第三章  有限长单位冲激响应(FIR)数字滤波器.....................................10
3.1  FIR滤波器的窗函数法设计 .................................................10
   3.1.1  窗函数法的基本思想..................................................10
   3.1.2  窗函数的种类 .......................................................11
3.2  FIR滤波器的最大误差最小化准则  ..........................................14
3.3  FIR滤波器的最大误差最小准则设计 .........................................15
3.4  FIR滤波器的优化设计 .....................................................17
第四章  无限长单位冲激响应(IIR)数字滤波器 ....................................22
4.1  IIR滤波器的s-z变换设计  .................................................22
4.1.1  标准z变换 .............................................................22
4.1.2  双线性z变换 ...........................................................23
4.2  IIR滤波器的振幅平方函数近似设计  ........................................24
4.3  IIR滤波器的频率变换法设计  ..............................................26
4.4  IIR数字滤波器的优化设计  ................................................27
第五章  总结  ................................................................33
致谢  ........................................................................34
参考文献  ....................................................................35