%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Adaptive Filter Theory 5e Solution Manual %% %% Chapter 7 %% Question 10 %% Parts a), b), and c) %% %% Program written to run on MATLAB 2010a (R) %% %% By Kelvin Hall %% July 2, 2014 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clearclcnumberOfDatapoints=100; % try 300 to get a better picture of the processnumberOfRuns=100; % The number of monteCarlo runs necissary for part d)aOne=0.1; %AR paramteraTwo=-0.8; %AR paramter as per textbook descriptionNoiseVariance=0.28;% The Noise variance found through part A of the problemNoiseStandardDeviation=sqrt(NoiseVariance);mu=0.2;delta=[0.5,0.25,0.75];u=zeros(numberOfDatapoints+3,1); % Allocate memory for input data streamf=zeros(numberOfDatapoints+3,1); % Allocate memory for error between % prediction and resutlsepsilonOne=zeros(numberOfDatapoints+3,1);% Allocate memory for error % between found weight and AR paramter 1epsilonTwo=zeros(numberOfDatapoints+3,1);% Allocate memory for error % between found weight and AR paramter 2J=zeros(numberOfDatapoints+3,1);% allocate memory for theoretical errorweights=zeros(2,numberOfDatapoints+3); % allocate memory for weightsfor ell=1:3 stream = RandStream('mt19937ar','Seed',2); % seed the random numberRandStream.setDefaultStream(stream); % generator for reproducable % resultsg=zeros(numberOfDatapoints+3,1);% allocate memory for squared-averaged errorfor k=1:numberOfRuns % increment through the monte carlo runs of the problem W=zeros(2,numberOfDatapoints+3); % reset the weights to zero between % each montecarlo run for n=3:numberOfDatapoints+3 u(n)=aOne*u(n-1)+aTwo*u(n-2)+randn(1)*NoiseStandardDeviation; % create a new piece of input data to the filter f(n)=u(n)-W(1,n-1)*u(n-1)-W(2,n-1)*u(n-2); % Caluclate error between desired result and predicted results W(:,n)=W(:,n-1)+(mu/(delta(ell)+u(n-1)^2+u(n-2)^2)*([u(n-1);u(n-2)]*f(n))); %update the weights as per LMS e(:,n)=W(:,n)-[u(n-1);u(n-2)]; end g=g+f.^2; % accumulate squared error of estimationendg=g/numberOfRuns; % accumulate squared error of estimationindex=1:numberOfDatapoints+3; %the x axis of the plotsubplot(3,3,1+(ell-1)*3)plot(index,W(1,:))xlim([0 numberOfDatapoints+3])ylim([-0.1, 0.5])str=sprintf('error in tap weight 1 estimate for delta = %.2f',delta(ell));title(str)xlabel('Iterations')ylabel('error between weight and AR paramter') subplot(3,3,2+(ell-1)*3) plot(index,W(2,:))xlim([0 numberOfDatapoints+3])str=sprintf('error in tap weight 2 estimate for delta = %.2f',delta(ell));title(str)xlabel('Iterations') ylabel('error between weight and AR paramter') subplot(3,3,3+(ell-1)*3) plot(index,g(1:numberOfDatapoints+3))xlim([0 numberOfDatapoints+3])ylim([0 1])xlabel('Number of iterations')ylabel('Squared Error')str=sprintf('Plot of Normalized LMS learning curve with delta =%.2f',delta(ell));title(str);end