《DSP using MATLAB》Problem 5.38

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.38 \n\n');

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

% ------------------------------------------------------------------------
%       1  x(n) = [2sin(0.04pi*n)+5cos(0.08pi*n)]
%                    N=40    N=50   N=60
%
% ------------------------------------------------------------------------
N = 40;
nn1 = [0:N-1];
xx1 = 2*sin(0.04*pi*nn1)+5*cos(0.08*pi*nn1);
NN1 = length(xx1);                                % length 

%m = mod_1(nn1, NN1);
%x = [xx1 zeros(1, 0)];                        % padding zeros
%n = [nn1 max(nn1)+1:max(nn1)+6];
x = xx1;
n = nn1;

str = fprintf('P5.38.1 x(n) N=%d', N);
figure('NumberTitle', 'off', 'Name', str);
set(gcf,'Color','white');
subplot(2,1,1); stem(nn1, xx1);
xlabel('n'); ylabel('x(n)');
title('x(n) ori sequence');  grid on;
subplot(2,1,2); stem(n, x);
xlabel('n'); ylabel('x(n)');
title('x(n) padding 0 zeros');  grid on;

%% =============================================================================
%%                 DTFT X(w) of xn sequence, w=[0:2pi],
%% =============================================================================
MM = 500;
[Xw_DTFT, w] = dtft1(x, n, MM);

 magXw_DTFT = abs(Xw_DTFT);   angXw_DTFT = angle(Xw_DTFT)/pi;
realXw_DTFT = real(Xw_DTFT); imagXw_DTFT = imag(Xw_DTFT);

%% --------------------------------------------------------------
%%        START X_DTFT's  mag ang real imag
%% --------------------------------------------------------------
figure('NumberTitle', 'off', 'Name', 'P5.38.1 X(w) DTFT of x(n) N=40');
set(gcf,'Color','white');
subplot(2,2,1); plot(w/pi,magXw_DTFT); grid on;  % axis([-2,2,0,15]);
title('Magnitude Part');
xlabel('frequency in \pi units'); ylabel('Magnitude  |X\_DTFT|');
subplot(2,2,3); plot(w/pi, angXw_DTFT); grid on;  % axis([-2,2,-1,1]);
title('Angle Part');
xlabel('frequency in \pi units'); ylabel('Rad \pi'); %axis([-200,200,0,2]);

subplot('2,2,2'); plot(w/pi, realXw_DTFT); grid on;
title('Real Part');
xlabel('frequency in \pi units'); ylabel('Real');
subplot('2,2,4'); plot(w/pi, imagXw_DTFT); grid on;
title('Imaginary Part');
xlabel('frequency in \pi units'); ylabel('Imaginary');
%% --------------------------------------------------------------
%%        END X_DTFT's  mag ang real imag
%% --------------------------------------------------------------

%% ------------------------------------------------------------------
%%                 DFT(k) of xn sequence, k=[0:N-1]
%%                      w=2pi*k/N       k=Nw/(2pi)
%% ------------------------------------------------------------------
N1 = length(x);
k1 = [0 : N1-1];
%k2 = [-N : N-1];
%k3 = [-N/2 : N/2];
Xk_DFT = dft(x, N1);                                         % 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);

figure('NumberTitle', 'off', 'Name', 'P5.38.1 DFT(k) of x(n) N=40')
set(gcf,'Color','white');
subplot(2,1,1); stem(k1, magXk_DFT); hold on; plot(N1*w/(2*pi), magXw_DTFT,'r--'); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of x(n)');  grid on;
subplot(2,1,2); stem(k1, angXk_DFT);  hold on; plot(N1*w/(2*pi), angXw_DTFT,'r--'); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of x(n)'); grid on;

%% =============================================================================
%%                 DTFT X(w) of xn sequence, w=[-2pi:2pi],
%% =============================================================================
MM = 500;
[Xw_DTFT, w] = dtft2(x, n, MM);

 magXw_DTFT = abs(Xw_DTFT);   angXw_DTFT = angle(Xw_DTFT)/pi;
realXw_DTFT = real(Xw_DTFT); imagXw_DTFT = imag(Xw_DTFT);

%% --------------------------------------------------------------
%%        START X_DTFT's  mag ang real imag
%% --------------------------------------------------------------
figure('NumberTitle', 'off', 'Name', 'P5.38.1 X(w) DTFT of x(n) N=40');
set(gcf,'Color','white');
subplot(2,2,1); plot(w/pi,magXw_DTFT); grid on;  % axis([-2,2,0,15]);
title('Magnitude Part');
xlabel('frequency in \pi units'); ylabel('Magnitude  |X\_DTFT|');
subplot(2,2,3); plot(w/pi, angXw_DTFT); grid on;  % axis([-2,2,-1,1]);
title('Angle Part');
xlabel('frequency in \pi units'); ylabel('Rad \pi'); %axis([-200,200,0,2]);

subplot('2,2,2'); plot(w/pi, realXw_DTFT); grid on;
title('Real Part');
xlabel('frequency in \pi units'); ylabel('Real');
subplot('2,2,4'); plot(w/pi, imagXw_DTFT); grid on;
title('Imaginary Part');
xlabel('frequency in \pi units'); ylabel('Imaginary');
%% --------------------------------------------------------------
%%        END X_DTFT's  mag ang real imag
%% --------------------------------------------------------------

%% ------------------------------------------------------------------
%%                 DFT(k) of xn sequence, k=[-N:N-1]
%%                    w=2pi*k/N       k=Nw/(2pi)
%% ------------------------------------------------------------------
N2 = length(x);
%k1 = [0 : length(x)-1];
k2 = [-N2 : N2-1];
%k3 = [-N/2 : N/2];
Xk_DFT = dft(x, N2);                                                % DFT
    magXk_DFT = abs( [ Xk_DFT Xk_DFT] );                           % DFT magnitude
    angXk_DFT = angle( [Xk_DFT Xk_DFT] )/pi;                       % DFT angle
   realXk_DFT = real([Xk_DFT Xk_DFT]);
   imagXk_DFT = imag([Xk_DFT Xk_DFT]);

figure('NumberTitle', 'off', 'Name', 'P5.38.1 DFT(k) of x(n) N=40')
set(gcf,'Color','white');
subplot(2,1,1); stem(k2, magXk_DFT); hold on; plot(N2*w/(2*pi), magXw_DTFT,'r--'); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of x(n)');  grid on;
subplot(2,1,2); stem(k2, angXk_DFT); hold on; plot(N2*w/(2*pi), angXw_DTFT,'r--'); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of x(n)');  grid on;

%% =============================================================================
%%                 DTFT X(w) of xn sequence, w=[-pi:pi],
%% =============================================================================
MM = 500;
[Xw_DTFT, w] = dtft3(x, n, MM);

 magXw_DTFT = abs(Xw_DTFT);   angXw_DTFT = angle(Xw_DTFT)/pi;
realXw_DTFT = real(Xw_DTFT); imagXw_DTFT = imag(Xw_DTFT);

%% --------------------------------------------------------------
%%        START X_DTFT's  mag ang real imag
%% --------------------------------------------------------------
figure('NumberTitle', 'off', 'Name', 'P5.38.1 X(w) DTFT of x(n) N=40');
set(gcf,'Color','white');
subplot(2,2,1); plot(w/pi,magXw_DTFT); grid on;  % axis([-2,2,0,15]);
title('Magnitude Part');
xlabel('frequency in \pi units'); ylabel('Magnitude  |X\_DTFT|');
subplot(2,2,3); plot(w/pi, angXw_DTFT); grid on;  % axis([-2,2,-1,1]);
title('Angle Part');
xlabel('frequency in \pi units'); ylabel('Rad \pi'); %axis([-200,200,0,2]);

subplot('2,2,2'); plot(w/pi, realXw_DTFT); grid on;
title('Real Part');
xlabel('frequency in \pi units'); ylabel('Real');
subplot('2,2,4'); plot(w/pi, imagXw_DTFT); grid on;
title('Imaginary Part');
xlabel('frequency in \pi units'); ylabel('Imaginary');
%% --------------------------------------------------------------
%%        END X_DTFT's  mag ang real imag
%% --------------------------------------------------------------

%% ------------------------------------------------------------------
%%                 DFT(k) of xn sequence, k=[-N/2:N/2]
%%                    w=2pi*k/N       k=Nw/(2pi)
%% ------------------------------------------------------------------
N3 = length(x);
%k1 = [0 : length(x)-1];
%k2 = [-N : N-1];
k3 = [-N3/2 : N3/2];
Xk_DFT = dft(x, N3);                                                   % DFT
    magXk_DFT = abs( [ Xk_DFT(N3/2+1 : N3) Xk_DFT(1 : N3/2+1)] );        % DFT magnitude
    angXk_DFT = angle( [Xk_DFT(N3/2+1 : N3) Xk_DFT(1 : N3/2+1)] )/pi;    % DFT angle
%   realXk_DFT = real([Xk_DFT(N/2+1 : N) Xk_DFT(1 : N/2+1)]);
%   imagXk_DFT = imag([Xk_DFT(N/2+1 : N) Xk_DFT(1 : N/2+1)]);

figure('NumberTitle', 'off', 'Name', 'P5.38.1 DFT(k) of x(n) N=40')
set(gcf,'Color','white');
subplot(2,1,1); stem(k3, magXk_DFT); hold on; plot(N3*w/(2*pi), magXw_DTFT,'r--'); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFT magnitude of x(n)');  grid on;
subplot(2,1,2); stem(k3, angXk_DFT); hold on; plot(N3*w/(2*pi), angXw_DTFT,'r--'); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFT angle of x(n)');  grid on;

　　运行结果：

下面是N=50的情况，附图