现代数字信号处理仿真作业

实用标准文档文案大全现代数字信号处理仿真作业1.仿真题3.17仿真结果及图形：图1基于FFT的自相关函数计算实用标准文档文案大全图3周期图法和BT法估计信号的功率谱图2基于式3.1.2的自相关函数的计算实用标准文档文案大全图4利用LD迭代对16阶AR模型的功率谱估计16阶AR模型的系数为：a1=-0.402637623107952-0.919787323662670i;a2=-0.013530139693503+0.024214641171318i;a3=-0.074241889634714-0.088834852915013i;a4=0.027881022353997-0.040734794506749i;a5=0.042128517350786+0.068932699075038i;a6=-0.0042799971761507+0.028686095385146i;a7=-0.048427890183189-0.019713457742372i;a8=0.0028768633718672-0.047990801912420ia9=0.023971346213842+0.046436389191530i;a10=0.026025963987732+0.046882756497113i;a11=-0.033929397784767-0.0053437929619510i;a12=0.0082735406293574-0.016133618316269i;a13=0.031893903622978-0.013709547028453i;a14=0.0099274520678052+0.022233240051564i;a15=-0.0064643069578642+0.014130696335881i;a16=-0.061704614407581-0.077423818476583i.仿真程序（3_17）:clearallclc%%产生噪声序列N=32;%基于FFT的样本长度实用标准文档文案大全%N=256;%周期图法，BT法，AR模型功率谱估计的长度vn=(randn(1,N)+1i*randn(1,N))/sqrt(2);%%产生复正弦信号f=[0.150.170.26];%归一化频率SNR=[303027];%信噪比A=10.^(SNR./20);%幅度signal=[A(1)*exp(1i*2*pi*f(1)*(0:N-1));%复正弦信号A(2)*exp(1i*2*pi*f(2)*(0:N-1));A(3)*exp(1i*2*pi*f(3)*(0:N-1))];%%产生观察样本un=sum(signal)+vn;%%利用3.1.1的FFT估计Uk=fft(un,2*N);Sk=(1/N)*abs(Uk).^2;r0=ifft(Sk);r1=[r0(N+2:2*N),r0(1:N)];%%利用3.1.2估计Rr2=xcorr(un,N-1,'biased');%画图k=-N+1:N-1;figure(1)subplot(1,2,1)stem(k,real(r1))xlabel('m');ylabel('实部');subplot(1,2,2)stem(k,imag(r1))xlabel('m');ylabel('虚部');figure(2)subplot(1,2,1)stem(k,real(r2))xlabel('m');ylabel('实部');subplot(1,2,2)stem(k,imag(r2))xlabel('m');ylabel('虚部');%%周期图法NF=1024;Spr=fftshift((1/NF)*abs(fft(un,NF)).^2);kk=-0.5+(0:NF-1)*(1/(NF-1));Spr_norm=10*log10(abs(Spr)/max(abs(Spr)));%%BT法M=64;r3=xcorr(un,M,'biased');BT=fftshift(fft(r3,NF));实用标准文档文案大全BT_norm=10*log10(abs(BT)/max(abs(BT)));figure(3)subplot(1,2,1)plot(kk,Spr_norm)xlabel('w/2pi');ylabel('归一化功率谱/DB');title('周期图法')subplot(1,2,2)plot(kk,BT_norm)xlabel('w/2pi');ylabel('归一化功率谱/DB');title('BT法')%%LD迭代算法p=16;r0=xcorr(un,p,'biased');r4=r0(p+1:2*p+1);%计算自相关函数a(1,1)=-r4(2)/r4(1);sigma(1)=r4(1)-(abs(r4(2))^2)/r4(1);form=2:p%LD迭代算法k(m)=-(r4(m+1)+sum(a(m-1,1:m-1).*r4(m:-1:2)))/sigma(m-1);a(m,m)=k(m);fori=1:m-1a(m,i)=a(m-1,i)+k(m)*conj(a(m-1,m-i));endsigma(m)=sigma(m-1)*(1-abs(k(m))^2);endPar=sigma(p)./fftshift(abs(fft([1,a(p,:)],NF)).^2);%p阶AR模型的功率谱Par_norm=10*log10(abs(Par)/max(abs(Par)));figure(4)plot(kk,Par_norm)xlabel('w/2pi');ylabel('归一化功率谱/DB');title('16阶AR模型')实用标准文档文案大全2.仿真题3.20仿真结果及图形：单次Root-MUSIC算法中最接近单位圆的两个根为：-0.001156047541561+1.001503153449793i0.587376604261220-0.810845628739986i对应的归一化频率为：0.250183714447964-0.150223406926494相同信号的MUSIC谱估计结果如下图5对3.20信号进行MUSIC谱估计的结果仿真程序（3_20）:clearallclc%%信号样本和高斯白噪声的产生N=1000;vn=(randn(1,N)+1i*randn(1,N))/sqrt(2);signal=[exp(1i*0.5*pi*(0:N-1)+1i*2*pi*rand);%复正弦信号exp(-1i*0.3*pi*(0:N-1)+1i*2*pi*rand)];un=sum(signal)+vn;%%计算自相关矩阵M=8;实用标准文档文案大全fork=1:N-Mxs(:,k)=un(k+M-1:-1:k).';endR=xs*xs'/(N-M);%%自相关矩阵的特征值分解[U,E]=svd(R);%%Root-MUSIC算法的实现G=U(:,3:M);Gr=G*G';co=zeros(2*M-1,1);form=1:Mco(m:m+M-1)=co(m:m+M-1)+Gr(M:-1:1,m);endz=roots(co);ph=angle(z)/(2*pi);err=abs(abs(z)-1);%%计算MUSIC谱En=U(:,2+1:M);NF=2048;forn=1:NFAq=exp(-1i*2*pi*(-0.5+(n-1)/(NF-1))*(0:M-1)');Pmusic(n)=1/(Aq'*En*En'*Aq);endkk=-0.5+(0:NF-1)*(1/(NF-1));Pmusic_norm=10*log10(abs(Pmusic)/max(abs(Pmusic)));plot(kk,Pmusic_norm)xlabel('w/2*pi');ylabel('归一化功率谱/dB')实用标准文档文案大全3.仿真题3.21仿真结果及图形：单次ESPRIT算法中最接近单位元的两个特征值为：0.001826505974929+1.000690248438859i0.586994191014025-0.809491260856630i对应的归一化频率为：0.249709503383161-0.150146235268272仿真程序（3_21）:clearallclc%%信号样本和高斯白噪声的产生N=1000;vn=(randn(1,N)+1i*randn(1,N))/sqrt(2);signal=[exp(1i*0.5*pi*(0:N-1)+1i*2*pi*rand);%复正弦信号exp(-1i*0.3*pi*(0:N-1)+1i*2*pi*rand)];un=sum(signal)+vn;%%自相关矩阵的计算M=8;fork=1:N-Mxs(:,k)=un(k+M-1:-1:k).';endRxx=xs(:,1:end-1)*xs(:,1:end-1)'/(N-M-1);Rxy=xs(:,1:end-1)*xs(:,2:end)'/(N-M-1);%%特征值分解[U,E]=svd(Rxx);ev=diag(E);emin=ev(end);Z=[zeros(M-1,1),eye(M-1);0,zeros(1,M-1)];Cxx=Rxx-emin*eye(M);Cxy=Rxy-emin*Z;%%广义特征值分解[U,E]=eig(Cxx,Cxy);z=diag(E);ph=angle(z)/(2*pi);err=abs(abs(z)-1);实用标准文档文案大全4.仿真题4.18仿真结果及图形：步长为0.05时失调参数为m1=0.0493；步长为0.005时失调参数为m2=0.0047。图6步长为0.05时权向量的收敛曲线图7步长为0.005时权向量的收敛曲线实用标准文档文案大全图8步长分别为0.05和0.005时100次独立实验的学习曲线仿真程序（4_18）:clearallclc%%产生100组独立样本序列data_len=512;trials=100;n=1:data_len;a1=-0.975;a2=0.95;sigma_v_2=0.0731;v=sqrt(sigma_v_2)*randn(data_len,1,trials);u0=[00];num=1;den=[1,a1,a2];Zi=filtic(num,den,u0);u=filter(num,den,v,Zi);%产生100组独立信号%%LMS迭代mu1=0.05;mu2=0.005;w1=zeros(2,data_len,trials);w2=w1;form=1:100;temp=zeros(data_len,1);e1(:,:,m)=temp;e2(:,:,m)=temp;d1(:,:,m)=temp;d2(:,:,m)=temp;forn=3:data_len-1实用标准文档文案大全w1(:,n+1,m)=w1(:,n,m)+mu1*u(n-1:-1:n-2,:,m)*conj(e1(n,1,m));w2(:,n+1,m)=w2(:,n,m)+mu2*u(n-1:-1:n-2,:,m)*conj(e2(n,1,m));d1(n+1,1,m)=w1(:,n+1,m)'*u(n:-1:n-1,:,m);d2(n+1,1,m)=w2(:,n+1,m)'*u(n:-1:n-1,:,m);e1(n+1,1,m)=u(n+1,:,m)-d1(n+1,1,m);e2(n+1,1,m)=u(n+1,:,m)-d2(n+1,1,m);endendt=1:data_len;w1_mean=zeros(2,data_len);w2_mean=w1_mean;e1_mean=zeros(data_len,1);e2_mean=e1_mean;form=1:100w1_mean=w1_mean+w1(:,:,m);w2_mean=w2_mean+w2(:,:,m);e1_mean=e1_mean+e1(:,:,m)