IIR數(shù)字低通濾波器的設(shè)計與實(shí)現(xiàn)

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摘要 當(dāng)前我們正處于數(shù)字化時代，數(shù)字信號處理技術(shù)受到了人們的廣泛關(guān)注，其理論及算法隨著計算機(jī)技術(shù)和微電子技術(shù)的發(fā)展得到了飛速的發(fā)展，被廣泛應(yīng)用于多種領(lǐng)域。數(shù)字濾波器是數(shù)字信號處理中最重要的組成部分之一，幾乎出現(xiàn)在所有的數(shù)字信號處理系統(tǒng)中。相對于模擬濾波器，數(shù)字濾波器沒有漂移，能夠處理低頻信號，頻率響應(yīng)特性可做成非常接近于理想的特性，且精度可以達(dá)到很高，容易集成等，這些優(yōu)勢決定了數(shù)字濾波器的應(yīng)用越來越廣泛。本文概述了IIR 數(shù)字濾波器設(shè)計的一般方法和步驟，分析了數(shù)字濾波器的實(shí)現(xiàn)方法。介紹了一種實(shí)現(xiàn)IIR數(shù)字濾波器的設(shè)計的方法，分別利用脈沖響應(yīng)不變法和雙線性變換法，運(yùn)用MATLAB編程設(shè)計IIR數(shù)字低通濾波器，并選擇了三種混合波形對已經(jīng)設(shè)計好的IIR數(shù)字低通濾波器進(jìn)行濾波性能驗(yàn)證，結(jié)果顯示濾波效果良好；IIR數(shù)字濾波器在語音、圖像、數(shù)字通信系統(tǒng)和計算機(jī)領(lǐng)域信號處理中有廣泛用途。本文結(jié)合IIR數(shù)字濾波器在圖像處理中的實(shí)例，研究了基于MATLAB數(shù)字濾波器設(shè)計與仿真問題。對巴特沃斯數(shù)字低通濾波器在圖像處理中的應(yīng)用進(jìn)行了實(shí)現(xiàn)，分別改變巴特沃斯低通濾波器的階數(shù)，對不同階數(shù)對濾波效果的影響進(jìn)行了對比分析，從而得出了一些重要結(jié)論。巴特沃斯濾波器階數(shù)不同，濾波效果也不一樣，階數(shù)越高，在阻頻帶振幅衰減速度越快。同樣的濾波器，階數(shù)越高值越均勻，濾波效果越好。
關(guān)鍵詞： IIR數(shù)字低通濾波器 MATLAB 脈沖響應(yīng)不變法 雙線性變換法 圖像處理

Design and implementation of IIR digital low pass filter
Abstract Currently we are in the digital era, digital signal processing technology has been widespread concern, with the development of the theory and algorithms of computer technology and microelectronics technology has been rapid development, has been widely used in many fields. The digital filter is part of digital signal processing, one of the most important, in almost all digital signal processing system. With respect to the analog filter, the digital filter does not drift to handle low-frequency signal, the frequency response characteristic can be made very close to the ideal characteristics, and can achieve a high precision, easy integration, determines the application of these advantages of digital filters more widely. This paper outlines the general approach and steps IIR digital filter, analyze the implementation method of the digital filter. Describes two methods to achieve IIR digital filter design, namely the use of impulse response method and bilinear transformation method, using MATLAB programming design IIR digital low-pass filter, and select three wave mixing has been designed for good IIR digital low-pass filter to filter the performance verification, the results show a good filter effect; IIR digital filter has many uses in speech, image, digital communication systems and signal processing in the computer field. In this paper, IIR digital filter in image processing examples studied based on MATLAB digital filter design and simulation problems. Butterworth low-pass filter in digital image processing were achieved, namely to change the order Butterworth low-pass filter, the effects of different filtering effect of the order to carry out a comparative analysis of the thus obtained Some important conclusions. Different order Butterworth filter, the effect of the filter is not the same. The lower the order of the filter is , the higher the filter order is, the faster the amplitude attenuated in the stop band . The same filter, the higher the value, the more uniform the order, the better filtering effect.
Keywords: IIR digital low-pass filter MATLAB Impulse response method Bilinear transformation method The image processing

目錄
第一章 緒論 1
1.1數(shù)字濾波器的研究背景與意義 1
1.2數(shù)字濾波器的應(yīng)用現(xiàn)狀與發(fā)展趨勢 2
1.3數(shù)字濾波器的定義和分類 3
1.4數(shù)字濾波器的實(shí)現(xiàn)方法分析 5
第二章 IIR數(shù)字低通濾波器的設(shè)計 6
2.1 IIR數(shù)字濾波器結(jié)構(gòu) 6
2.2 IIR數(shù)字濾波器的設(shè)計過程 9
2.2.1用脈沖響應(yīng)不變法設(shè)計IIR數(shù)字低通濾波器 9
2.2.2 用雙線性變換法設(shè)計IIR數(shù)字低通濾波器 11
第三章IIR數(shù)字低通濾波器濾波器的MATLAB實(shí)現(xiàn) 14
3.1 MATLAB簡介及優(yōu)勢 14
3.2 MATLAB在數(shù)字濾波器中常用命令及函數(shù) 15
3.3 基于MATLAB的IIR低通數(shù)字濾波器的設(shè)計步驟 16
第四章 IIR數(shù)字低通濾波器的綜合設(shè)計與仿真 18
4.1 經(jīng)典設(shè)計法設(shè)計IIR數(shù)字低通濾波器 18
4.2 IIR數(shù)字低通濾波器的設(shè)計與仿真 20
4.3 數(shù)字低通濾波器在圖像處理中的設(shè)計及仿真 26
結(jié)論和展望 33
致謝 34
參考文獻(xiàn) 35