How to find the Fourier coefficients, NEED HELP

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!!

[Torsten]

Use the definition of the Fourier coefficients and MATLAB's "integral".

[Paul]

As previously shown in this comment, that equation for S is not correct for turning F(t) into the specified periodic function.

Answer 1

[Ranjeet]

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.