Matlab 周期方波信號傅里葉級數展開

方波信號為：

傅里葉級數展開為：

程序運行結果：

程序代碼：

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