基于双线性变换法的IIR数字高通滤波器设计

摘要

随着信息时代和数字世界的到来，数字信号处理已成为当今一门极其重要的学科和技术领域。在数字信号处理中起着重要的作用并已获得广泛应用的是数字滤波器（DF，Digital Filter）。数字滤波器是一种用来过滤时间离散信号的数字系统，通过对抽样数据进行数学处理来达到频域滤波的目的。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。

本次主要利用matlab的信号处理工具箱设计一个数字高通IIR滤波器，并用此滤波器处理一段音频信号。此报告重点介绍了用双线性不变法设计IIR数字滤波器的基本流程，比较了各种设计方法的优缺点，总结了模拟滤波器的性能特征。最后以双线性不变法设计了一个高通巴特沃斯IIR数字滤波器，介绍了设计步骤，然后在Matlab环境下进行了仿真与调试，实现了设计

目标。

关键字 IIR数字滤波器巴特沃斯高通双线性变换 MATLAB

Abstract

With the information era and the advent of the digital world, digitalsignal processing has become one of the important vr漫游fields of science and technology. In the digital signal processing plays an陶崇斌 important role 油底壳垫and has been widely applied in the digital filter.手机光线传感器 Digital水貂肉带风扇的安全帽filter is a discrete time signal is used to filter the digital system,through the mathematical processing of sampling data to reach the goal of frequency domain filterin. Implementation of IIR filter order is low, less storage unit, with high efficiency, high precision, and can keep some simulation characteristics of filter, so a very wide application. Matlab software based on matrix computation, the calculation,visualization and program design of organic integration to interactive environment, and provides an intuitive, efficient, convenient tool for the research and application of digital filter..

The main use of signal processing toolbox of MATLAB to design a digital high-pass IIR filter, and an audio signal with the filter. This report focuses on the basic process of using the bilinearinvariant IIR digital filter design, compares the advantages and disadvantages of various design methods, summarizes thecharacteristics of the analog filter. Finally, by bilinear invariant to design a high Butterworth IIR digitalfilter, introduces the design steps, and then in the Matlab environment for the simulation and debugging, achieves the design goal.

Keywords IIR Butterworth high-pass bilinear transform MATLABdigital filter

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