《DSP using MATLAB》Problem 5.36-优快云博客

本文通过MATLAB实现离散傅立叶变换(DFT)，针对一个正弦序列进行分析，展示其幅值、相位及实虚部分的特性，并提供完整的代码与运行结果。

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，