【正文】 更為有希 望的形式，以便估計信號的特征參量，或削弱信號中的多余分量和增強信號中的有用分量。在數(shù)字計算器中完成所要求的傳輸函數(shù)運算之后，再通過數(shù)字 模擬轉換器和保持電路，使信號形成最后要求的波形。數(shù)字濾波器的功能是將一組輸入的數(shù)字序列通過一定的運算后轉變?yōu)榱硪唤M輸出的數(shù)字序列，因此它本身就是一臺數(shù)字式的處理設備。最后應用 FDATool 和 Simulink 工具對 IIR 數(shù)字濾波器進行了仿真。 本文由數(shù)字濾波器的功能、應用及發(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)字濾波器基本結構。數(shù)字濾波器工作在數(shù)字信號域，它處理的對象是經由采樣器件將模擬信號轉 換而得到的數(shù)字信號。 IIR 數(shù)字濾波器的設計 摘 要 數(shù)字濾波器是對數(shù)字信號進行濾波處理以得到期望的響應特性的離散時間系統(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域的模擬濾波器不同。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絡實現(xiàn)濾波功能；而前者是通過數(shù)字運算器件對輸入的數(shù)字信號進行運算和處理，從而實現(xiàn)設計要求的特性。其次根據(jù) IIR 數(shù)字濾波器的設計原理，在 MATLAB 環(huán)境下分別采用脈沖響應不變法、雙線性變換法和 MATLAB 函數(shù)直接設計法對 IIR 數(shù)字濾波器進行了設計。 關鍵詞 ： IIR數(shù)字濾波器 ； MATLAB； 脈沖響應不變法；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)字濾波器的實現(xiàn)方法 ......................................................................................................... 5 MATLAB 軟件簡介 ................................................................................................................ 6 MATLAB 的語言特點 ............................................................................................................ 8 第二章 數(shù)字濾波器基礎 ......................................................................................................... 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)字濾波器的基本結構 ................................................................................................. 12 直接 Ⅰ 型 ........................................................................................................................ 13 直接 Ⅱ 型 ........................................................................................................................ 14 級聯(lián)型 ............................................................................................................................ 14 并聯(lián)型 ............................................................................................................................ 16 第三章 IIR 數(shù)字濾波器的設計方法及過程 ...................................................................... 17 基于脈沖響應不變法的 IIR 濾波器設計 ............................................................................ 17 基于雙線性 Z 變換法的 IIR 濾波器設計 ........................................................................... 20 基于 MATLAB 函數(shù)直接設計 IIR 數(shù)字濾波器 ................................................................. 24 巴特沃斯數(shù)字濾波器設計 ............................................................................................ 24 切比雪夫 Ⅰ 型 IIR 數(shù)字濾波器設計 ............................................................................ 27 切比雪夫 Ⅱ 型 IIR 數(shù)字濾波器設計 ............................................................................ 29 基于橢圓法直接設計 IIR 數(shù)字濾波器 ........................................................................ 30 FDATOOL設計法 .................................................................................................................. 33 SIMULINK 建模設計法 .......................................................................................................... 37 第四章 結論 ................................................................................................................................. 41 參考文獻 ...................................................................................................................