how to plot the exponential fourier series in matlab?

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Daniel Niu
Daniel Niu 2022-10-19
评论： VBBV 2022-10-19
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));

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采纳的回答

VBBV
VBBV 2022-10-19
Ran in:
% (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)

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