%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 5.34 \n\n');

banner();

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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

%          X(k) is DFTs of real-valued sequence x(n)

%           x(n)=A*cos(2*pi*l*n/N)   n=[0:N-1]

%

%             1   x1(n) = 3cos(0.04*pi*n)  n=[0:200-1]

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

N = 200; l = 2;

n1 = [0:N-1];

x1 = 3*cos(2*pi*l*n1/100);

figure('NumberTitle', 'off', 'Name', 'P5.34.1 x(n), N=200')

set(gcf,'Color','white');

stem(n1, x1);

xlabel('n'); ylabel('x(n)');

title('x(n)=3cos(0.04*pi*n)');  grid on;

    k1 = [0:N-1];

Xk_DFT = fft(x1, N);

    N1 = length(Xk_DFT);                                              % length 

    magXk_DFT = abs( [ Xk_DFT ] );                                    % DFT magnitude

    angXk_DFT = angle( [Xk_DFT] )/pi;                                 % DFT angle

   realXk_DFT = real(Xk_DFT); imagXk_DFT = imag(Xk_DFT);

figure('NumberTitle', 'off', 'Name', 'P5.34.1 X(k), DFT of x(n) N=200')

set(gcf,'Color','white');

subplot(2,2,1); stem(k1, magXk_DFT);

xlabel('k'); ylabel('magnitude(k)');

title('magnitude DFT of x(n)');  grid on;

subplot(2,2,3); stem(k1, angXk_DFT);

%axis([-N/2, N/2, -0.5, 50.5]);

xlabel('k'); ylabel('angle(k)');

title('angle DFT of x(n)');  grid on;

subplot(2,2,2); stem(k1, realXk_DFT);

xlabel('k'); ylabel('real (k)');

title('real DFT of x(n)');  grid on;

subplot(2,2,4); stem(k1, imagXk_DFT);

%axis([-N/2, N/2, -0.5, 50.5]);

xlabel('k'); ylabel('imag (k)');

title('imag DFT of x(n)');  grid on;

figure('NumberTitle', 'off', 'Name', 'P5.34.1 real X(k), N=200')

set(gcf,'Color','white');

stem(k1, realXk_DFT);

xlabel('k'); ylabel('real (k)');

title('real DFT of x(n)');  grid on;