《DSP using MATLAB》Problem 5.36

第1小题

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.36 \n\n');
 
banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
% -------------------------------------------------------------------------------------
%          X(k) is DFTs of real-valued sequence x(n)
%           x(n)=A*sin(2*pi*l*n/N)      n=[0:N-1]
%
%             1   x1(n) = 3sin(0.04*pi*n)  n=[0:200-1]
% -------------------------------------------------------------------------------------
N = 200; l = 2;
n1 = [0:N-1];
x1 = 3*sin(2*pi*l*n1/100);
 
figure('NumberTitle', 'off', 'Name', 'P5.36.1 x(n), N=200')
set(gcf,'Color','white');
stem(n1, x1);
xlabel('n'); ylabel('x(n)');
title('x(n)=3sin(0.04\pin)');  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', 'P5.36.1 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', 'P5.36.1 Imagnary X(k), N=200')
set(gcf,'Color','white');
stem(k1, imagXk_DFT);
xlabel('k'); ylabel('imag (k)');
title('imag DFT of x(n)');  grid on;

　　运行结果：

200个样点包含4个周期，

序列的DFT

DFT序列的虚部，范围[0:N-1]。

DFT序列的实部和虚部，范围[-N:N-1]。

DFT序列的实部和虚部，范围[-N/2:N/2-1]。