how to plot the exponential fourier series in matlab?

I expand a periodic function exp(-t) with T=3.

then sum the series to compare with the original function. However, I think the oscillation

is too large. Where is the problem?

Your help would be highly appreciated.

Best regards.

% (a)plot x(t) over a time interval (0,3)
clear;clc
t = 0:0.01:3; % total simulation time
x = exp(-t);
plot(t,x,'r','LineWidth',2)
a=zeros(1,61);



for K=-30:30

  G=@(t)exp(-(t)).*exp(-1i*K*2*pi/3.*t);
  a(K+31)=1/3*quad(G,0,3);
end

x30 = 0.*t;
for j = 1:30
x30 = x30 + 2*real(a(j+31)*exp(1i*(j)*pi.*t/1.5));
end
x30=x30++a(31);
hold on
plot(t, x30,'b','LineWidth',2)





% plot(t,x1,'b','LineWidth',2)
% plot(t,abs(x2),'b','LineWidth',3)


%K=-30:30
%stem(K,abs(a));

Answer 1

[VBBV]

% (a)plot x(t) over a time interval (0,3)
clear;clc
t = 0:0.01:3; % total simulation time
x = exp(-t);
plot(t,x,'r','LineWidth',2)
a=zeros(1,61);



for K=-30:30

  G=@(t)exp(-(t)).*exp(-1i*K*2*pi/3.*t);
  a(K+31)=1/3*integral(G,0,3);
end

x30 = 0.*t;
for j = 1:30
x30 = x30 + 2*real(a(j+31)*exp(1i*(j)*pi.*t/1.5));
end
x30=x30++a(31);
hold on
plot(t, x30,'b','LineWidth',2)

[VBBV]

Try with

a(K+31)=1/3*integral(G,0,3);

instead of

a(K+31)=1/3*quad(G,0,3);

[Daniel Niu]

Thank you so much for your explanation! Thank you!

[VBBV]

Please accept the answer if it solved your problem