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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 5.22 \n\n');

banner();

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

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

%          512-point DFT of a real-valued sequence x(n)

%

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

 k = [0:511];

Xk_DFT = [zeros(1, 512)];

Xk_DFT(0+1) = 20;    Xk_DFT(5+1) = 20+j*30;    Xk_DFT(32+1) = -10+j*15;   Xk_DFT(152+1) = 17+j*23;

Xk_DFT(256+1) = 30;  Xk_DFT(360+1) = 17-j*23;  Xk_DFT(480+1) = -10-j*15;  Xk_DFT(507+1) = 20-j*30;

 N = length(Xk_DFT);

    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);

EXk = sum(abs(Xk_DFT).^2)/N

 x = real(idft(Xk_DFT, N));

 n = [0:N-1];

figure('NumberTitle', 'off', 'Name', 'P5.22 X(k), DFT of x(n)')

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

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

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

title('magnitude DFT of x(n), N=512');  grid on;

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

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

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

title('angle DFT of x(n), N=512');  grid on;

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

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

title('real DFT of x(n), N=512');  grid on;

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

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

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

title('imag DFT of x(n), N=512');  grid on;   

figure('NumberTitle', 'off', 'Name', 'P5.22 x(n)')

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

%subplot(3,1,1);

stem(n, x);

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

title('x(n), N=512');  grid on;