How to find the Fourier coefficients, NEED HELP

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Mohammad Sharifi
Mohammad Sharifi 2023-4-3
回答： Ranjeet 2023-4-11
Hi,
I have the signal:
F(t) = te^(2t), -2 < t < 2 , The Period T = 4.
I have to graph this for, -5 <= t <= 6, which I have the following code for:
clear all
clc
F = @(t) t.*exp(2*t);
T = 4;
t = linspace(-5,6,1000);
S = F(mod(t, T) - T/2 );
plot(t, S);
xlabel('t');
ylable('F(t)');
Now I have make a code to find the Fourier coefficients C0, C1, C2 and C3.
Can anyone Help?
Thank You In advance!!
  2 个评论
Torsten
Torsten 2023-4-3
Use the definition of the Fourier coefficients and MATLAB's "integral".
Paul
Paul 2023-4-3
As previously shown in this comment, that equation for S is not correct for turning F(t) into the specified periodic function.

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回答（1 个）

Ranjeet
Ranjeet 2023-4-11
Ran in:
Hi Sharifi,
Following is the code to get the required coefficients c0, c1, c2 and c4 for the mentioned signal ‘S’.
clear all
clc
syms t;
% Exponential function F
F = @(t) t.*exp(2*t);
% Required time period T
T = 4;
% Periodic function S, created from F
S = F(mod(t, T) - T/2);
fplot(S, [-5, 6]);
xlabel('t');
ylabel('S(t)');
% Uncomment the following code to test with sine and/or cosine signals
% S = sin(t);
% T = 2*pi;
c0 = int(S, -T/2, T/2)/T;
% cn is a 4x1 vector have the required 4 coefficients c0, c1, c2 and c3.
cn = zeros(1,4);
cn(1) = c0;
for n = 1:3
an = int(S*cos(2*pi*n*t/T), -T/2, T/2)*2/T;
bn = int(S*sin(2*pi*n*t/T), -T/2, T/2)*2/T;
cn(n+1) = (an - 1i*bn)/2;
end
cn
cn =
10.2429 + 0.0000i 7.9449 + 4.5829i 4.3542 + 5.2942i 2.4458 + 4.5360i
Also, you can refer to the following answer related to Fourier Series - https://www.mathworks.com/matlabcentral/answers/66040-calculating-fourier-series-coefficients.

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