Matlab 周期方波信号傅里叶级数展开

方波信号为：

傅里叶级数展开为：

程序运行结果：

程序代码：

 clear

 x = -6:0.01:6;
 T = 4;

 f = x;
 for N = 1:length(f)
     temp = rem(abs(x(N)),T);
     if temp>1 && temp<3
         f(N) = 0;
     else
         f(N) = 1;
     end
 end

 % f(x) = 1/2 + sum(g(k,x))   (k=1,2,3,4......)
 % g(k,x) = sinc(k/2)*cos(k*pi/2*x)
 % MATLAB build-in function: sinc(x) = sin(x*pi)/(x*pi)

 count = 9;
 y = zeros(count, length(x));

 for N = 1:count
     k = 2*N-1;
     if N==1
         y(N,:) = 0.5 + sinc(k/2)*cos(k*pi/2*x);
     else
         y(N,:) = y(N-1,:) + sinc(k/2)*cos(k*pi/2*x);
     end
 end

 row = ceil(sqrt(count));
 colomn = ceil(count/row);
 for N=1:count
     subplot(row,colomn,N);
     plot(x,f,'k');
     hold on
     h = plot(x,y(N,:),'r');
     title(strcat(num2str(2*N-1),' harmonic'));
 end