[毕业设计 论文 精品]基于lms和rls的自适应滤波器的应用仿真

计算机与通信学院基于LMS和RLS的自适应滤波器应用仿真1.自适应滤波原理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，主要由参数可调的数字滤波器和自适应算法两部分组成，如图1所示a11a2a0a3a4a5a6a7a8a1x(n)称为输入信号，y(n)称为输出信号，d(n)称为期望信号或者训练信号，e(n)为误差僖号，其中，e(n)=d(n)-y(n).自适应滤波器的系数(权值)根据误差信号e(n)，通过一定的自适应算法不断的进行改变，以达到使输出信号y(n)最接近期望信号图中参数可调的数字滤波器和自适应算法组成自适应滤波器。自适应滤波算法是滤波器系数权值更新的控制算法，根据输入信号与期望信号以及它们之间的误差信号，自适应滤波算法依据算法准则对滤波器的系数权值进行更新，使其能够使滤波器的输出趋向于期望信号。原理记数字滤波器脉冲响应为g726g75(g78)=g62g75a9(g78)g75a10(g78)g258g75a11a12a10(g78)g64a13输入g18331g7691信号为a14x(g78)=g62x(g78)x(g78-g20)g258x(g78-n-g20)g64误差信号为a14)()()(kykyke=()()()()Tekykhkxk=g1260化过g12255g4613是最g4579化性能指g7643J(k),它是误差的g5191g7053和g72621()()()()kTiJkyihkxi=g8726使J(k)最g4579的系数向g18339h(k),g2375使J(k)对h(k)的g4560数为g19658，g1075g4613是0)()(=kdhkdJ。g6238g45(g78)的g15932达g5347g1207入，得g72612()()()()0kTiyihkxixi=和11()()()()()kkTTTiixiyihkxixi=由g8504得出滤波器系数的最g1260向g18339g72611()()()()()kTTikTixiyihkxixi=g17837g1022g15932达g5347由输入信号自g11468g1863g11709g19465()xxcx和输入信号与参g13783信号的g11468g1863g11709g19465()yxck组成，如g991所示，g13512数g18129为g708ng15ng709g291()()()kTxxickxixi=1()()()kTyxickxiyi=系数最g1260向g18339g1075可以g1901成如g991g5430g5347g7261()()()Toptyxxxhkckck=自g11468g1863和g1126g11468g1863g11709g19465的g17894g5414g15932达g5347如g991g726()(1)()()Txxxxckckxkxk=+()(1)()()Tyxyxckckykxk=+g6238()yxck的g17894g5414g15932达g5347g1207入系数向g18339g15932达g5347，得g7261()()()Tyxxxhkckck=g23751()(1)()()()TTyxxxhkckxkykck=+g13783g15397到(1)(1)(1)Tyxxxckhkck=可以记1()()(1)(1)()()xxxxhkcxckhkykxk=+用前g19766得到的g15932达g5347g8726出(1)xxck，g5194g1207入g990g5347g7261()()()()()(1)()()Txxxxhkcxckxkxkhkykxk=+或1()(1)()()()()()(1)Txxhkhkcxykxkxkxkhk=+则滤波器系数的g17894g5414g1863系g5347可以记g13281()(1)()()()()()(1)Txxhkhkcxykxkxkxkhk=+其中()()()(1)Tekykxkhk=e(g78)g15932示g1820g20576误差。g2494g3252为它是由前一g1022g18331g7691时刻的系数算出的，g3324g4466g19481中，g5468g3822时g1517由于g75(g78)g16757算的g3809g7446g5242g13792不能应用于g4466时控制。用g165g15g44g1207g6454()xxck，其中g726g165为自适应g7811g5242，g44为g17788g16794g11709g19465g708n，ng709g17837时()(1)()()xhkhkkek=+g17837时g4613是一g1022最g4579g3355g7053准则g19394g20076。2.LMS自适应滤波器举例自回归过程的自适应预估器自g3250g5414过g12255是用g7481g6563g17860g1288随一g1135可能性g16280g5471出g10628的g13491g16757g10628g16949的g11648时g1284g16757的随机过g12255。一g19466自g3250g5414g8181g3423的g1856g5347如g991g7261()(1)()ykaykbk=+1aa15a16a17a18a19a20a21a22a23b(k)a15a24a25a26a27a28a29a30a31a20a32a33a34a35a36a37a38a39a40a20a32a41a42a43a21a221aa44a45a20a46a47a48a18a20a49a33a34a35a47a50a38a30LMSa51a52a41a53a54a55a56a57a58a59a60)1()()(1=kykykea)()1()()1(11kekykkaa+=+a61Na32a62a50a63a21a221a,a64a65a61a66a25a26a67a68Ma69a30a70a71a72a73a43a74a75a76a77a76a78a23a74a75a76a77a76a79a23a74a75a76a77a78a44a45a63a51a30a21a221aa80a81a82a83a76a77a84a30a57a85a86a87a54a55a60a88a75a79a76a76a89a90a75a91a76a89a92a75a78a89a93a78a75a83a76a77a94a89a95a75a96a97a98a99a100a101a90a102a92a103a78a102a104a105a89a97a75a96a97a98a99a100a101a90a102a92a102a104a105a89a106a99a98a107a75a78a108a104a109a106a107a75a75a78a107a97a110a111a93a75a76a77a76a78a89a97a110a100a97a107a97a110a111a93a75a76a77a76a79a112a101a107a83a78a105a89a97a92a107a89a106a99a98a113a75a78a108a90a114a75a76a77a91a112a98a93a92a107a92a101a78a102a88a105a89a115a101a78a105a75a78a89a106a99a98a109a75a91a108a88a115a101a109a105a75a83a93a78a112a115a101a109a83a78a105a103a114a101a109a105a89a97a92a107a106a99a98a109a75a92a103a78a108a88a97a101a113a102a109a102a107a105a75a115a101a109a105a83a95a101a113a102a109a102a107a105a112a115a101a109a83a78a105a89a95a101a113a102a109a103a78a102a107a105a75a95a101a113a102a109a102a107a105a103a107a97a110a111a93a112a115a101a109a83a78a105a112a97a101a113a102a109a102a107a105a89a97a92a107a97a92a107a97a92a107a106a99a98a107a75a78a108a104a106a99a98a109a75a78a108a88a97a116a101a109a102a107a105a75a76a89a95a116a101a109a102a107a105a75a76a89a106a99a98a117a75a78a108a90a97a116a101a109a102a107a105a75a97a116a101a109a102a107a105a103a97a101a117a102a109a102a107a105a118a91a89a95a116a101a109a102a107a105a75a95a116a101a109a102a107a105a103a95a101a117a102a109a102a107a105a89a97a92a107a97a92a107a97a92a107a106a109a119a120a98a97a101a78a105a100a97a116a109a110a99a119a115a101a78a108a78a79a76a102a97a116a101a78a108a78a79a76a102a78a105a105a102a95a99a110a107a99a92a100a97a116a109a110a99a119a115a101a78a108a78a79a76a102a97a116a101a78a108a78a79a76a102a91a105a102a121a98a121a105a102a95a99a110a107a99a92a100a97a116a109a110a99a119a115a101a78a108a78a79a76a102a97a116a101a78a108a78a79a76a102a104a105a102a121a119a121a105a102a95a99a110a107a99a106a106a93a122a109a100a101a123a76a78a79a76a76a77a76a78a78a124a105a102a119a98a109a107a111a109a111a110a97a101a121a90a97a93a92a100a125a120a93a98a97a97a98a98a99a98a121a105a122a110a93a114a97a110a101a121a126a93a116a127a110a97a100a121a105a119a111a97a122a111a101a121a128a110a97a106a111a93a98a98a99a129a107a75a76a77a76a78a121a105a89a119a111a97a122a111a101a121a128a110a97a106a111a93a98a98a99a129a107a75a76a77a76a79a121a105a89a119a111a97a122a111a101a121a128a110a97a106a111a93a98a98a99a129a107a75a76a77a78a121a105a89a106a109a119a120a98a97a101a91a105a102a127a110a99a111a101a78a108a88a102a95a116a101a78a108a88a102a78a105a105a102a95a99a110a107a99a92a127a110a99a111a101a78a108a88a102a95a116a101a78a108a88a102a91a105a102a121a98a121a105a102a95a99a110a107a99a92a127a110a99a111a101a78a108a88a102a95a116a101a78a108a88a102a104a105a102a121a119a121a105a102a95a99a110a107a99a106a106a102a119a98a109a107a111a109a111a110a97a101a121a130a109a110a111a97a98a131a99a97a106a106a131a109a97a92a111a97a132a93a110a120a111a109a99a92a121a105a122a110a93a114a97a110a101a121a126a93a116a127a110a97a100a121a105a102a119a111a97a122a111a101a121a107a75a76a77a76a78a121a105a102a119a111a97a122a111a101a121a107a75a76a77a76a79a121a105a102a119a111a97a122a111a101a121a107a75a76a77a78a121a105a133a134a18a54a55a135a136a137a60a1372.a66a25a56a138a139a138a1373.a36a37a38a140a22a141a142系数以时间g5132数的指数g7366g13459g6922g6959，g165g17246g3835，时间g5132数g17246g45793.RLS自适应滤波器的应用仿真从噪声中提取信号输入信号为g726000()cos()()xkAwtbk=+其中g69(g78)是g19480g2164的g11345噪声。000()cos()rxkAwt=+a143a144a145RLSa146a147a143a148a149a150a151a152a153a154a155a156a157a158a15911(1)()()1()(1)()xxTxxckxkgkxkckxk=+a146a147a143a160a161a162a163a164a165a166a167a168a169a165a170a171a172()()(1)()Tekykhkxk=a173a174a175a176()(1)()()hkhkgkek=+a146a147a143a148a149a150a177a178a162a163a164a165a166a167a1681,na171111()(1)()()(1)Txxxxxxckckgkxkck=a179a180a181a182a183a184a185a186a151a146a187a188a189a190a191a192a165a166a167a168a169a193a170a171()()()Tykhkxk=a146a147a143a148a149a179a194所研究的滤波器阶数为200，采样周期等于1ms.程序清单如下：N=1000;n=200;k=12;Ts=1e-1b=0.8*randn(1,N);fori=1:Nxr(1,i)=sin(k*2*pi*i/N);x(1,i)=xr(1,i)+b(i);endCxx=10000*eye(n);g=zeros(N,n);h=zeros(N,n);e=zeros(1,N);y=zeros(1,N);tr=zeros(1,N);fori=n+1:Ng(i,:)=(Cxx*x(i-n+1:i)./(1+x(i-n+1:i)*Cxx*x(i-n+1:i);e(1,i)=xr(i)-h(i-1,:)*x(i-n+1:i);h(i,:)=h(i-1,:)+e(1,i)*g(i,:);Cxx=Cxx-g(i,:)*x(i-n+1:i)*Cxx;y(1,i)=h(i,:)*x(i-n+1:i);tr(1,i)=trace(Cxx);endfigure(1)plot(0:N-n,x(1,n:N),gridtitle(x(k)inputsingnalinV)xlabel(Samples)figure(2)plot(0:N-n,xr(1,n:N),r),gridaxis(0800-1.21.2)title(xr(k)referencesingnalinV)xlabel(Samples)figure(3)plot(0:N-n,e(1,n:N),holdonplot(0:N-n,y(1,n:N),r),holdongridtitle(e(k)errorandy(k)outputinV)xlabel(Samples)gtext(e(k),gtext(y(k)figure(4)plot(