《DSP using MATLAB》Problem 5.17

1、代码

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.17 \n\n');

banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

% -------------------------------------------------------------------------------------
%          X(k) is 10-point DFTs of real-valued sequence x(n)
%          X(k) = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j]
%               N = 10       k=[0:9]
%             1   y(n) = x((2-n))10
% -------------------------------------------------------------------------------------

    k1 = [0:9];
Xk_DFT = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j];
    N1 = length(Xk_DFT);                                              % length is 10

    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', 'P5.17.1 X(k), DFT of x(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magXk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of x(n), N=10');  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), N=10');  grid on;
subplot(2,2,2); stem(k1, realXk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of x(n), N=10');  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), N=10');  grid on;

[xn] = real(idft(Xk_DFT, N1));                     % real-valued sequence
n = [0 : N1-1];

% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
%         1st way to get y(n)-----circular shifft
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
xn_cirfold = xn(mod(-n,N1)+1);
m = 2;                                         % shift
yn1 = cirshftt(xn_cirfold, m, length(xn));

Xfk_DFT = dft(xn_cirfold, N1);
    magXfk_DFT = abs( [ Xfk_DFT ] );                          % DFT magnitude
    angXfk_DFT = angle( [Xfk_DFT] )/pi;                       % DFT angle
   realXfk_DFT = real(Xfk_DFT); imagXfk_DFT = imag(Xfk_DFT);

figure('NumberTitle', 'off', 'Name', 'P5.17.1 X((-k)), DFT of x((-n))')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magXfk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of x((-n)), N=10');  grid on;
subplot(2,2,3); stem(k1, angXfk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of x((-n)), N=10');  grid on;
subplot(2,2,2); stem(k1, realXfk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of x((-n)), N=10');  grid on;
subplot(2,2,4); stem(k1, imagXfk_DFT);
axis([0, 10, -5, 5.05]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of x((-n)), N=10');  grid on;

% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
%       2ed way to get y(n)-----IDFT of Y(k)
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
k1 = [0:9];
Yk_DFT = exp(-j*2*pi*(2*k1)/10) .* Xk_DFT(mod(-k1, N1)+1);
    N1 = length(Yk_DFT);                                    % length is 10

    magYk_DFT = abs( [ Yk_DFT ] );                          % DFT magnitude
    angYk_DFT = angle( [Yk_DFT] )/pi;                       % DFT angle
   realYk_DFT = real(Yk_DFT); imagYk_DFT = imag(Yk_DFT);

figure('NumberTitle', 'off', 'Name', 'P5.17.1 DFT(k) of y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magYk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of y(n), N=10');  grid on;
subplot(2,2,3); stem(k1, angYk_DFT);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of y(n), N=10');  grid on;
subplot(2,2,2); stem(k1, realYk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of y(n), N=10');  grid on;
subplot(2,2,4); stem(k1, imagYk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of y(n), N=10');  grid on;

[yn2] = real(idft(Yk_DFT, N1));
n = [0 : N1-1];

figure('NumberTitle', 'off', 'Name', 'P5.17.1 x(n) & y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(n, xn);
xlabel('n'); ylabel('x(n)');
title('x(n), IDFT of X(k)');  grid on;
subplot(2,2,2); stem(n, yn1);
xlabel('n'); ylabel('y(n)');
title('y(n) by circular shift x((2-n))_N N=10');  grid on;
subplot(2,2,3); stem(n, xn_cirfold);
xlabel('n'); ylabel('x((-n))');
title('x((-n)) N=10');  grid on;
subplot(2,2,4); stem(n, yn2);
xlabel('n'); ylabel('y(n)');
title('y(n) by IDFT of Y(k)');  grid on;

　　运行结果：

4、代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.17 \n\n');

banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

% -------------------------------------------------------------------------------------
%          X(k) is 10-point DFTs of real-valued sequence x(n)
%          X(k) = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j]
%               N = 10       k=[0:9]
%             4   y(n) = x(n) Circular-Conv x((-n))10
% -------------------------------------------------------------------------------------

    k1 = [0:9];
Xk_DFT = [10, -2+3j, 3+4j, 2-3j, 4+5j, 12, 4-5j, 2+3j, 3-4j, -2-3j];
    N1 = length(Xk_DFT);                                              % length is 10

    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', 'P5.17.4 X(k), DFT of x(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magXk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of x(n), N=10');  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), N=10');  grid on;
subplot(2,2,2); stem(k1, realXk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of x(n), N=10');  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), N=10');  grid on;

[xn] = real(idft(Xk_DFT, N1));                     % real-valued sequence
n = [0 : N1-1];

% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
%         1st way to get y(n)-----circular
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
xn_cirfold = xn(mod(-n,N1)+1);
       yn1 = circonvt(xn, xn_cirfold, N1);

% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
%       2ed way to get y(n)-----IDFT of Y(k)
% +++++++++++++++++++++++++++++++++++++++++++++++++++++++
k1 = [0:9];
Xfk_DFT = dft(xn_cirfold, N1);

Yk_DFT = Xk_DFT .* Xfk_DFT;
    N1 = length(Yk_DFT);                                    % length is 10

    magYk_DFT = abs( [ Yk_DFT ] );                          % DFT magnitude
    angYk_DFT = angle( [Yk_DFT] )/pi;                       % DFT angle
   realYk_DFT = real(Yk_DFT); imagYk_DFT = imag(Yk_DFT);

figure('NumberTitle', 'off', 'Name', 'P5.17.4 DFT(k) of y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(k1, magYk_DFT);
xlabel('k'); ylabel('magnitude(k)');
title('magnitude DFT of y(n), N=10');  grid on;
subplot(2,2,3); stem(k1, angYk_DFT);
xlabel('k'); ylabel('angle(k)');
title('angle DFT of y(n), N=10');  grid on;
subplot(2,2,2); stem(k1, realYk_DFT);
xlabel('k'); ylabel('real (k)');
title('real DFT of y(n), N=10');  grid on;
subplot(2,2,4); stem(k1, imagYk_DFT);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of y(n), N=10');  grid on;

[yn2] = real(idft(Yk_DFT, N1));
n = [0 : N1-1];

figure('NumberTitle', 'off', 'Name', 'P5.17.4 x(n) & y(n)')
set(gcf,'Color','white');
subplot(2,2,1); stem(n, xn);
xlabel('n'); ylabel('x(n)');
title('x(n), IDFT of X(k)');  grid on;
subplot(2,2,2); stem(n, yn1);
xlabel('n'); ylabel('y(n)');
title('y(n) by x(n) Circular-Conv x((-n))_N N=10');  grid on;
%subplot(2,2,3); stem(n, xn_cirfold);
%xlabel('n'); ylabel('x((-n))');
%title('x((-n)) N=10');  grid on;
subplot(2,2,4); stem(n, yn2);
xlabel('n'); ylabel('y(n)');
title('y(n) by IDFT of Y(k)');  grid on;

　　运行结果：