【 MATLAB 】使用 MATLAB 比较占空比不同的周期方波的 DFS 图

周期方波的表达式我就不提炼了，既然你来看文章了，我就不信你周期方波都不知道。

占空比定义为：L/N，N为周期，下面我们对 L = 5，N = 20； L = 5，N = 40；L = 5，N = 60；L = 7，N = 60分别画出它们的DFS图作比较。

我觉得有必要先把对应的周期方波给出来（每幅图都只给出一个周期）：

  

   

    

     

    
    

     

      clc;clear;close all;
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 5,N = 20
     
    
   

    

     

    
    

     

      L = 5;
     
    
   

    

     

    
    

     

      N = 20;
     
    
   

    

     

    
    

     

      n = 0:N-1;
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      subplot(2,2,1)
     
    
   

    

     

    
    

     

      stem(n,xn);
     
    
   

    

     

    
    

     

      title('L = 5,N = 20');
     
    
   

    

     

    
    

     

      xlabel('n');ylabel('xtilde(n)');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 5,N = 40
     
    
   

    

     

    
    

     

      L = 5;
     
    
   

    

     

    
    

     

      N = 40;
     
    
   

    

     

    
    

     

      n = 0:N-1;
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      subplot(2,2,2)
     
    
   

    

     

    
    

     

      stem(n,xn);
     
    
   

    

     

    
    

     

      title('L = 5,N = 20');
     
    
   

    

     

    
    

     

      xlabel('n');ylabel('xtilde(n)');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 5,N = 60
     
    
   

    

     

    
    

     

      L = 5;
     
    
   

    

     

    
    

     

      N = 60;
     
    
   

    

     

    
    

     

      n = 0:N-1;
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      subplot(2,2,3)
     
    
   

    

     

    
    

     

      stem(n,xn);
     
    
   

    

     

    
    

     

      title('L = 5,N = 20');
     
    
   

    

     

    
    

     

      xlabel('n');ylabel('xtilde(n)');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 7,N = 60
     
    
   

    

     

    
    

     

      L = 7;
     
    
   

    

     

    
    

     

      N = 60;
     
    
   

    

     

    
    

     

      n = 0:N-1;
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     

      subplot(2,2,4)
     
    
   

    

     

    
    

     

      stem(n,xn);
     
    
   

    

     

    
    

     

      title('L = 5,N = 20');
     
    
   

    

     

    
    

     

      xlabel('n');ylabel('xtilde(n)');
     
    
   

    

     

    
    

     
 
     
    
  
 

上面程序中的DFS函数定义在另一篇博文中：【 MATLAB 】离散傅里叶级数（DFS）及 IDFS 的 MATLAB 实现

直接给出MATLAB脚本：

  

   

    

     

    
    

     

      clc;clear;close all;
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 5,N = 20
     
    
   

    

     

    
    

     

      L = 5;
     
    
   

    

     

    
    

     

      N = 20;
     
    
   

    

     

    
    

     

      k = [-N/2:N/2];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     

      Xk = dfs(xn,N);
     
    
   

    

     

    
    

     

      magXk = abs( [ Xk(N/2+1:N),Xk(1:N/2+1) ] );
     
    
   

    

     

    
    

     

      subplot(2,2,1)
     
    
   

    

     

    
    

     

      stem(k,magXk);
     
    
   

    

     

    
    

     

      title('DFS of Square: L = 5,N = 20');
     
    
   

    

     

    
    

     

      xlabel('k');ylabel('Xtilde(k)');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 5,N = 40
     
    
   

    

     

    
    

     

      L = 5;
     
    
   

    

     

    
    

     

      N = 40;
     
    
   

    

     

    
    

     

      k = [-N/2:N/2];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     

      Xk = dfs(xn,N);
     
    
   

    

     

    
    

     

      magXk = abs( [ Xk(N/2+1:N),Xk(1:N/2+1) ] );
     
    
   

    

     

    
    

     

      subplot(2,2,2)
     
    
   

    

     

    
    

     

      stem(k,magXk);
     
    
   

    

     

    
    

     

      title('DFS of Square: L = 5,N = 40');
     
    
   

    

     

    
    

     

      xlabel('k');ylabel('Xtilde(k)');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 5,N = 60
     
    
   

    

     

    
    

     

      L = 5;
     
    
   

    

     

    
    

     

      N = 60;
     
    
   

    

     

    
    

     

      k = [-N/2:N/2];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     

      Xk = dfs(xn,N);
     
    
   

    

     

    
    

     

      magXk = abs( [ Xk(N/2+1:N),Xk(1:N/2+1) ] );
     
    
   

    

     

    
    

     

      subplot(2,2,3)
     
    
   

    

     

    
    

     

      stem(k,magXk);
     
    
   

    

     

    
    

     

      title('DFS of Square: L = 5,N = 60');
     
    
   

    

     

    
    

     

      xlabel('k');ylabel('Xtilde(k)');
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      % Periodic square wave parameters L = 7,N = 60
     
    
   

    

     

    
    

     

      L = 7;
     
    
   

    

     

    
    

     

      N = 60;
     
    
   

    

     

    
    

     

      k = [-N/2:N/2];
     
    
   

    

     

    
    

     
 
     
    
   

    

     

    
    

     

      xn = [ones(1,L),zeros(1,N-L)];
     
    
   

    

     

    
    

     

      Xk = dfs(xn,N);
     
    
   

    

     

    
    

     

      magXk = abs( [ Xk(N/2+1:N),Xk(1:N/2+1) ] );
     
    
   

    

     

    
    

     

      subplot(2,2,4)
     
    
   

    

     

    
    

     

      stem(k,magXk);
     
    
   

    

     

    
    

     

      title('DFS of Square: L = 7,N = 60');
     
    
   

    

     

    
    

     

      xlabel('k');ylabel('Xtilde(k)');
     
    
   

    

     

    
    

     
 
     
    
  
 

文章来源: reborn.blog.csdn.net，作者：李锐博恩，版权归原作者所有，如需转载，请联系作者。

原文链接：reborn.blog.csdn.net/article/details/83450759