本科毕业设计（论文）
题 目 基于MATLAB的希尔伯 特FIR滤波器设计_ 姓 名 专 业 电子科学与技术 学 号 指导教师 张庆辉
郑州科技学院电气工程学院 二○一四年五月
目 录
摘 要 ............................................................................................................................ I ABSTRACT .................................................................................................................. II 前言 ..............................................................................................................................IV 1 设计的目的与意义 .................................................................................................... 1 2 Matlab概述 ............................................................................................................. 3
2.1 MATLAB语言的发展 .................................................................................. 3 2.2 MATLAB的主要功能 .................................................................................. 3 2.3 matlab的程序结构 ........................................................................................ 4 3 希尔伯特变换的基本原理 ........................................................................................ 5
3.1希尔伯特变换的定义 ....................................................................................... 6
3.1.1 卷积积分 ................................................................................................ 6 3.1.2 ?2相位 ................................................................................................ 6 3.1.3 解析信号的虚部 .................................................................................... 7 3.2 希尔伯特变换的性质 ...................................................................................... 8
3.2.1 线性性质 ................................................................................................ 8 3.2.2 移位性质 ................................................................................................ 8 3.2.3 希尔伯特变换的希尔伯特变换 ............................................................ 8 3.2.4 逆希尔伯特变换 .................................................................................... 8 3.2.5 奇偶特性 ................................................................................................ 9 3.2.6 能量守恒 ................................................................................................ 9 3.2.7 正交性质 ................................................................................................ 9 3.2.8 调制性质 ................................................................................................ 9 3.2.9 卷积性质 .............................................................................................. 10
4 Fir滤波器的基本原理及设计方法 ...................................................................... 11
4.1 Fir滤波器的基本原理及其特点 ................................................................... 12
4.1.1 FIR数字滤波器的基本原理 ............................................................... 12 4.1.2 FIR滤波器的基本特点 ....................................................................... 12
4.2 FIR数字滤波器的设计 ................................................................................. 13 5 希尔伯特fir滤波器 ................................................................................................ 14 6 希尔伯特变换的应用 .............................................................................................. 18
6.1 希尔伯特变换在探地雷达数据处理中的应用 ............................................ 18
6.1.1 公式 ...................................................................................................... 18 6.1.2 算法 ...................................................................................................... 19 6.2 数字I-Q下变频器 ........................................................................................ 20
6.2.1 希尔伯特变换 ...................................................................................... 21 6.2.2 基于希尔伯特变换的数字I-Q下变频器 .......................................... 22 6.3 希尔伯特变换在解调中的应用 .................................................................... 22
6.3.1 希尔伯特变换 ...................................................................................... 22 6.3.2 在解调中的应用 .................................................................................. 23 6.3.3 解调性能分析 ...................................................................................... 24
7 希尔伯特变换器的Matlab设计 ............................................................................ 26
7.1 直接程序法 .................................................................................................... 26 7.2 利用FDATool工具设计法 ........................................................................... 27 7.3 希尔伯特变换器的效果验证 ........................................................................ 31 结论 .............................................................................................................................. 33 前景展望 ...................................................................................................................... 34 致 谢 .......................................................................................................................... 35 参 考 文 献 ................................................................................................................ 36 附录 .............................................................................................................................. 37
基于MATLAB的希尔伯特FIR滤波器设计
基于MATLAB的希尔伯特FIR滤波器设计
摘 要
在通信系统中，经常需要对一个信号进行正交分解,即分解为同相分量和正交分量，并能有效地提取复杂信号的瞬时参数——瞬时振幅、瞬时相位和瞬时频率。希尔伯特变换器是幅频特性为1的全通滤波器，信号通过希尔伯特变化器后，其负频率成分作正90度相移，而正频率成分作负90度相移。因此希尔伯特变换在数字信号处理理论和应用中有着十分重要的作用，维系着对离散序列进行傅里叶变换后的实部和虚部之间或者幅度和相位之间的关系。而且在通过计算对低通滤波器的系数进行转换，其计算繁琐且存在一定的误差。Matlab作为滤波器设计的基础软件，具有强大的数学运算能力、方便实用的绘图功能及语言的高度集成性，它在其他科学与工程领域的应用也是越来越广，并且有着更广阔的应用前景和无穷无尽的潜能。
论文则主要是介绍了希尔伯特FIR滤波器的设计思想与步骤，通过建立滤波器模型利用MATLAB软件进行仿真，在计算机辅助计算基础上分析滤波器结构和参数的字长对其性能指标的影响。
本论文的设计思想是通过对FIR滤波器、希尔伯特变换器与MATLAB软件进行分别阐述和分析，来达到对希尔伯特fir滤波器整体的理解与设计，同时又通过对其应用的分析来加深对其的理解。
关键词：Matlab；希尔伯特变换器；FIR滤波器；FDATool工具
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基于MATLAB的希尔伯特FIR滤波器设计
HILBERT FIR FILTER DESIGN BASED ON
MATLAB
Abstract
In a communication system, often need to orthogonal decomposition of a signal,
namely decomposition for in-phase component and quadrature component, and can effectively extract the instantaneous parameters of the complex signal, instantaneous amplitude, instantaneous phase and instantaneous frequency.Hilbert transformer is amplitude frequency characteristics of 1 all-pass filter, signal through Hilbert changes after its negative frequency components are 90 degree phase shift, and is making negative 90 degree phase shift frequency components.So the Hilbert transform in digital signal processing has a very important role in theory and application, sustained by Fourier transform of discrete sequence after or between the real and imaginary part of the relationship between the amplitude and phase.And through the calculation of low pass filter coefficient, its computation complex and there are some error.Matlab as the basis of filter design software, with a strong mathematical operation ability, convenient and practical drawing function and the language highly integration, it's on the other is also more and more widely used in the field of science and engineering, and has a broad application prospect and endless potential.
Paper has mainly introduced the design idea and steps of Hilbert FIR filter, by filter model is set up using MATLAB software, the simulation is based on computer aided calculation analysis filter structure and parameters of word length effect on its performance.
Design idea of this paper is based on FIR filter with MATLAB software, the Hilbert transformer expounds and analysis respectively, to achieve the overall
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