摘要：等波纹最佳逼近法是滤波器设计方法中的一种，它克服了FIR(有限长单位冲激响应)数字滤波器设计的傅里叶级数法（窗函数设计法）和频率采样法存在的缺点，使得最大误差（即波纹的峰值）最小化，并且在整个逼近频段上呈现均匀分布。等波纹的含义是：幅频响应在阻带和通带上都是呈现等波纹的。最佳逼近指的则是在滤波器的长度已经给定的条件下，这种设计方法能使加权误差波纹幅度达到最小化。我们甚至可以分别控制阻带和通带的波纹幅度。将它和窗函数设计法、频率采样法相比较，用等波纹最佳逼近法设计的数字滤波器的性价比最高。当设计指标相同时，它能使滤波器的阶数最低；当阶数相同时，它能使通带最平坦，阻带最小而衰减最大；而且因为通带和阻带都是等波纹形式，所以最适合用来设计片段常数特性的滤波器。本篇论文主要是研究基于matlab的等波纹最佳逼近FIR数字滤波器设计，采用了数值分析中的remez多重交换迭代算法来求解等波纹最佳逼近问题，以求出满足等波纹最佳逼近准则的FIR数字滤波器的单位脉冲响应h（n）。在matlab平台上将运用窗函数法和等波纹最佳逼近法设计的数字带通滤波器的幅频特性曲线图绘制在一起可以清晰地看出运用等波纹最佳逼近法设计出的滤波器的幅频响应在阻带和通带上都是呈现等波纹的。

关键词：FIR数字滤波器;MATLAB;迭代算法;等波纹

Abstract：Equiripple approximation is an optimal filter design method, which overcomes the FIR (finite impulse response) digital filter design of the Fourier series method (window function design method and frequency sampling method) shortcomings, so that the maximum error (i.e. ripple peak) is minimized, and has uniform distribution in the whole approximation of the spectrum.Equiripple approximation for wave pattern meaning is: the best approximation of FIR digital filter method the design of the frequency response in the stop-band and pass-band are presented such as corrugated, and we can control  the stop-band and pass-band ripple amplitude. Compared with the window function design method and frequency sampling method, the digital filter with the  best  ripple approximation method has the highest cost performance.When the design index is the same, it can make the filter order minimum;When the order is the same, it can make the passband most flat and the stopband minimum and decay the maximum;Moreover, since passband and stop band are all ripple shapes, the filter is most suitable for designing the property of the fragment constant.This thesis is mainly about the design of FIR digital filter based on equal ripple optimal approximation of MATLAB,the Remez multiple exchange iterative algorithm in numerical analysis is used to solve the optimal approximation problem,in order to  satisfy  the optimum approximation  principle of equal  ripple,  the unit     impulse response h（ n） of FIR digital filter satisfying the best approximation principle of equal ripple is obtained.In the MATLAB platform, using the amplitude frequency characteristic curve of the window function method and the optimal approximation corrugated design digital bandpass filter to draw together can be clearly seen by the best bellows approximation filter method to design the frequency response in the stopband and passband are presented such as corrugated.

Keywords: FIR digital filter; MATLAB; Remez function; ripple

目录

第一章绪论 1

1.1研究的背景与意义 1

1.2国内外研究现状 2

1.3本文的主要结构与要完成的任务 4

1.3.1本文的主要结构