【正文】 IIR 數(shù)字濾波器的設(shè)計(jì) 摘 要 數(shù)字濾波器是對(duì)數(shù)字信號(hào)進(jìn)行濾波處理以得到期望的響應(yīng)特性的離散時(shí)間系統(tǒng)。作為一種電子濾波器，數(shù)字濾波器與完全工作在模擬信號(hào)域的模擬濾波器不同。數(shù)字濾波器工作在數(shù)字信號(hào)域，它處理的對(duì)象是經(jīng)由采樣器件將模擬信號(hào)轉(zhuǎn) 換而得到的數(shù)字信號(hào)。數(shù)字濾波器的工作方式與模擬濾波器也完全不同：后者完全依靠電阻、電容、晶體管等電子元件組成的物理網(wǎng)絡(luò)實(shí)現(xiàn)濾波功能；而前者是通過數(shù)字運(yùn)算器件對(duì)輸入的數(shù)字信號(hào)進(jìn)行運(yùn)算和處理，從而實(shí)現(xiàn)設(shè)計(jì)要求的特性。 本文由數(shù)字濾波器的功能、應(yīng)用及發(fā)展入手，介紹了數(shù)字濾波器 的基本概念，其中包括系統(tǒng)的描述、系統(tǒng)的傳遞函數(shù)和 IIR 數(shù)字濾波器基本結(jié)構(gòu)。其次根據(jù) IIR 數(shù)字濾波器的設(shè)計(jì)原理，在 MATLAB 環(huán)境下分別采用脈沖響應(yīng)不變法、雙線性變換法和 MATLAB 函數(shù)直接設(shè)計(jì)法對(duì) IIR 數(shù)字濾波器進(jìn)行了設(shè)計(jì)。最后應(yīng)用 FDATool 和 Simulink 工具對(duì) IIR 數(shù)字濾波器進(jìn)行了仿真。 關(guān)鍵詞 ： IIR數(shù)字濾波器 ； MATLAB； 脈沖響應(yīng)不變法；雙線性變換法 ； FDATool； Simulink Design of IIR digital filter Abstract Digital filters are the discretetime systems that process to filter digital signal to get expected response characteristics. As an electronic filter, digital filters work differently from the analog signal filters who pletely work in analogy signal domain. Digital filter work in the digital signal domain and its targets are digital signals that are received by sampling devices converting analog signals to digital signals. The working methods of digital filters and analog filters are pletely different: the latter pletely rely on the function of the physical work formed by resistors, capacitors, transistors and other electronic ponents of filtering ,while the former putes and processes digital signals with the help of digital puting devices to realize the characteristics of the design requirements. In this paper, the function, application and development of the digital filter are introduced followed by the introduction of the principle of digital filter design. The principle first includes the description of the system, the transfer function of the system and the basic structure of the IIR (Infinite Impulse Response) digital filter. Then, according to the design principle of IIR digital filter, the IIR digital filter is designed by the method of nonchanging impulse response, the method of double linear transform and direct method using MATLAB functions. At last, the designed IIR digital filter is simulated by FDATool and MATLAB Simulink Tool. Key words: IIR digital filter； MATLAB； nonchanging impulse response； double linear transformation； FDATool； Simulink 目 錄 第一章 緒論 ................................................................................................................................... 1 數(shù)字濾波器技術(shù)概述 ............................................................................................................. 1 濾波器及濾波方法的發(fā)展歷程 ............................................................................................. 2 濾波器的分類 ......................................................................................................................... 3 數(shù)字濾波器的優(yōu)越性 ............................................................................................................. 4 數(shù)字濾波器的實(shí)現(xiàn)方法 ......................................................................................................... 5 MATLAB 軟件簡介 ................................................................................................................ 6 MATLAB 的語言特點(diǎn) ............................................................................................................ 8 第二章 數(shù)字濾波器基礎(chǔ) ......................................................................................................... 10 數(shù)字濾波器的基本概念 ....................................................................................................... 10 系統(tǒng)的描述 ........................................................................................................................... 11 系統(tǒng)的傳遞函數(shù) ................................................................................................................... 12 IIR 數(shù)字濾波器的基本結(jié)構(gòu) ................................................................................................. 12 直接 Ⅰ 型 ........................................................................................................................ 13 直接 Ⅱ 型 ........................................................................................................................ 14 級(jí)聯(lián)型 ............................................................................................................................ 14 并聯(lián)型 ............................................................................................................................ 16 第三章 IIR 數(shù)字濾波器的設(shè)計(jì)方法及過程 ...................................................................... 17 基于脈沖響應(yīng)不變法的 IIR 濾波器設(shè)計(jì) ............................................................................ 17 基于雙線性 Z 變換法的 IIR 濾波器設(shè)計(jì) ........................................................................... 20 基于 MATLAB 函數(shù)直接設(shè)計(jì) IIR 數(shù)字濾波器 ................................................................. 24 巴特沃斯數(shù)字濾波器設(shè)計(jì) ............................................................................................ 24 切比雪夫 Ⅰ 型 IIR 數(shù)字濾波器設(shè)計(jì) ............................................................................ 27 切比雪夫 Ⅱ 型 IIR 數(shù)字濾波器設(shè)計(jì) ............................................................................ 29 基于橢圓法直接設(shè)計(jì) IIR 數(shù)字濾波器 ........................................................................ 30 FDATOOL設(shè)計(jì)法 .................................................................................................................. 33 SIMULINK 建模設(shè)計(jì)法 .......................................................................................................... 37 第四章 結(jié)論 ................................................................................................................................. 41 參考文獻(xiàn) ........................................................................................................................................ 42 致 謝 ......................................................................................................................................