% ###################################################################################

% ## Code to be used after plot 4th fugure program ask user to input the mu value ##

% ## try use 0.01 for first Time to start estmated using function LMS ##

% ###################################################################################

clear all;

close all;

%% Part 1_A

N = 2000; %sampels

n = 0:N-1;

x=cos(0.03*pi*n);

figure(1);

stem(n,x);

xlabel('n');

ylabel('X[n]');

title('Part 1_A sequence of X[N] ');

%% ############################################################

% Part 1_B

C = [1, -2, 4]; %coefficient of unknown system(filter).

[F,w] = freqz(C,1,N);

figure(2);

%-------------------

subplot(2,1,1); %plot magnitude.

plot(w/pi,abs(F));

title('Magnitude');

%-------------------

subplot(2,1,2); %plot phase.

plot(w/pi,angle(F));

title('Phase');

%% ############################################################

% Part 1_C

spec = fft(x,N);

f = (0:N-1)/N;

figure(3);

stem(f,abs(spec));

xlabel('Normalized frequency (cycles/sample)');

ylabel('Amplitudde');

title('Spectrum of the input signal x[n]');

%% ############################################################

% Part 1_D

d = filter([1 -2 4],1,x); %find d(n).

figure(4);

subplot(2,1,1); %plot magnitude of d(n)

plot(n,abs(d));

title('Magnitude d(n)');

ylabel('Amplitude');

xlabel('n');

subplot(2,1,2); %plot phase of d(n)

plot(n,angle(d));

title('Phase d(n)');

ylabel('Amplitude');

xlabel('n');

%_______________________

L = 10; %read mu from user input.

S = sprintf('Enter the step -size factor mu (0 - %0.2f ): ',L);

mu = input(S);

%_______________________

%mu = 0.01; %can be changed as you want

w = zeros(1,4);

e = zeros(1,N);

J = zeros(1,N);

size = 4;

for n = size:length(x)

xn = x(n:-1:n-size+1);

y = xn * w.' ;

e(n) = d(n) - y;

w = w + 2* mu * e(n) * x(n:-1:n-size+1);

J(n) = e(n)^2;

end

%____________________________________________

% Plot the learning curves

% Plot the errror e(n).

figure(5);

plot(e);

title('Error vs Iteration Steps');

xlabel('Iteration Steps');

ylabel('Error');

%____________________________________________

% Plot (J vs iteration steps).

figure(6);

plot(J);

title('J vs Iteration Steps');

xlabel('Iteration Steps');

ylabel('J');

%____________________________________________

% Plot (10log10(J) vs iteration steps).

figure(7);

plot(10*log10(J));

title('10log10(J) vs Iteration Steps');

xlabel('Iteration Steps');

ylabel('10log10(J)');

%% ############################################################

% Part 1_E

%z = freqz(w,1);

[Z,s] = freqz(w,1,N);

figure(8);

subplot(2,1,1);

plot(abs(Z));

title('Magnitude Estimated FIR');

subplot(2,1,2);

plot(angle(Z));

title('Phase Estimated FIR');

%% ############################################################

% Part 1_F

% Repeat run code and change mu input from user

%% ############################################################

% Part 1_G

For this project i do the code which show in part B the filter if it high pass or low pass and so on

also in part E i plot the estimation

the good work is that must part B plot same as Part E plot Filter same but my code show real high pass but estimation part low pass is there problem in my code can u help me to find where is the error and solve it plz

Fig. 1 System Identification