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河南科技学院新科学院2014届本科毕业论文（设计）基于matlab自适应滤波器滤波器的设计及实现学生姓名：倪闯所在院系：新科学院电气工程系所学专业：电气工程及其自动化导师姓名：孔晓红完成时间：2014年4月10日基于matlab自适应滤波器滤波器的设计及实现摘要自适应滤波器的研究是当今自适应信号处理中最为活跃的研究课题之一。因其具有很强的自学习、自跟踪能力和算法的简单易实现性等优点，使得它在噪化信号的检测增强，噪声干扰的抵消，通信系统的自适应均衡，图像的自适应增强复原以及未知系统的自适应参数辩识等方面都得到了广泛的应用。自适应滤波器是指利用前一时刻的结果，自动调节当前时刻的滤波器参数，以适应信号和噪声未知或随机变化的特性，得到有效的输出。研究自适应滤波器可以去除输出信号中噪声和无用信息，得到失真较小或者完全不失真的输出信号。本文介绍了自适应滤波器的理论基础，重点讲述了自适应滤波器的几种实现结构，然后重点介绍了两种自适应滤波算法最小均方误差（LMS）算法和递推最小二乘（RLS）算法，并对LMS算法和RLS算法性能进行了详细的分析。其中LMS算法结构简单，鲁棒性强，但其收敛速度很慢，而RLS收敛速度快，但其运算量很大。最后本文对基于LMS算法和RLS算法的自适应滤波器进行MATLAB仿真应用，实验表明：在自适应信号处理中，自适应滤波信号占有很重要的地位，自适应滤波器应用领域广泛；另外LMS算法和RLS算法各有优缺点，LMS算法因其鲁棒性强特点而应用于自回归预测器，而RLS算法因其收敛速度快优点而应用于信号增强器中。关键词：自适应滤波器，LMS算法，matlab仿真DesignandImplemeutationoftheAuto-adaptedFilterAbstractTheadaptivefilterisoneofthemostactiveresearchtopicinadaptivesignalprocessingtoday.Becauseithasastrongself-learning,self-trackingcapabilitiesandalgorithmssimpleeaseofimplementation,etc.,makingitinthedetectioninthenoiseofthesignalenhancement,noiseoffset,communicationsystems,adaptiveequalization,adaptiveimageenhancedrecoveryandunknownadaptiveparameteridentificationhavebeenwidelyused.Adaptivefilterusingtheresultsoftheprevioustime,automaticallyadjustthefilterparametersforthecurrenttimetoadapttothecharacteristicsofsignalandnoiseisunknownorrandomvariation,theeffectiveoutput.Studytheadaptivefiltercanremovenoiseanduselessinformationoutputsignaldistortionsmallerorcompletelylosingthetrueoutputsignal.Thispaperfirstintroducesthetheoreticalbasisofthefilter,Secondly,tohighlightseveraloftheadaptivefilterstructure,andthenfocusesontwoadaptivefilteringalgorithmminimummeansquareerror(LMS)algorithmandrecursiveleastsquare(RLS)algorithm,LMSalgorithmsimplestructure,robustness,butitsconvergenceisveryslow,whiletheRLSconvergencespeed,butitscomputationalcomplexity.Finally,experimentsshowthat:MATLABsimulationapplicationsbasedontheLMSalgorithmandRLSadaptivefilteralgorithminadaptivesignalprocessing,adaptivefilteringsignaloccupiesaveryimportantpositioninthewidespreadapplicationsofadaptivefilters;LMSalgorithmadvantagesanddisadvantagesandRLSalgorithm,LMSalgorithmbecauseofitsstrongrobustnessfeaturesusedinautoregressivepredictor,whiletheRLSalgorithmisitsfastconvergencespeedadvantagesappliedtothesignalenhancer.Keywords:adaptivefilter,LMSalgorithm,matlabsimulationI目录绪论........................................................................................................................11选题背景............................................................................................................11.1研究目的和意义.....................................................................................11.2国内外研究现状与前景.........................................................................22自适应滤波器的基础理论................................................................................42.1模拟滤波器的基本理论.........................................................................42.2数字滤波器的基本理论.........................................................................52.2.1数字滤波器设计的基本步骤......................................................52.2.2数字滤波器的实现方法...............................................................62.2.3IIR和FIR数字滤波器特点比较分析........................................62.3自适应滤波器的基本理论.....................................................................82.4自适应滤波器的结构...........................................................................102.4.1自适应横向滤波器....................................................................10自适应横向滤波器的结构图如图2.3所示，)()........(),(10nwnwnwN为可调节抽头权系数表示在n时刻的系数值。它利用正规直接形式实现全零点传输函数，而不采用反馈调节。权系数的调节过程是首先自动调节滤波器系数的自适应训练步骤，然后利用滤波系数加权延迟抽头上的信号来产生输出信号，将输出信号与期望信号进行对比，所得的误差值通过一定的自适应控制算法再用来调整权值，以保证滤波器处在最佳状态，其抽头加权系数集正好等于它的冲激响应，达到实现滤波的目的。......................................................................................................................112.4.2自适应递归滤波器....................................................................112.4.3自适应各型滤波器....................................................................113自适应滤波算法..............................................................................................123.1LMS算法..............................................................................................123.1.1算法简介....................................................................................123.1.2原理介绍....................................................................................133.2RLS算法论述....................................................................................163.2.1算法简介....................................................................................163.2.2原理介绍....................................................................................173.3其他自适应滤波算法...........................................................................20II3.3.1仿射投影法................................................................................203.3.2共轭梯度算法............................................................................203.3.3基于子带分解的自适应滤波算法............................................213.3.4