# Fourier series of any function

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Vansh on 17 Nov 2022
Edited: Torsten on 17 Nov 2022
Can you give an example of how to do fourier series of any function in MATLAB?
Torsten on 17 Nov 2022
Edited: Torsten on 17 Nov 2022
Define a function handle to define the function you want the fourier coefficients of and evaluate the integrals to determine the Fourier coefficients either using "int" if you are confident to get analytic expressions or else "integral" to get numerical approximations. The latter approach will only be applicable to get partial sums of the Fourier series.

Star Strider on 17 Nov 2022
I am in no way certain what you want.
Calculating a numerical transform is straightforward, however calculating a symbolic version of the same function may not be possible because not all integrals have closed-form solutions.
An example of a numerical transform —
Fs = 250;
L = 150;
t = linspace(0, L-1, L)/Fs;
s = sin(2*pi*t*50) .* exp(-(t-0.3).^2 * 50);
Fn = Fs/2;
NFFT = 2^nextpow2(L);
FTs = fft(s(:).*hann(L), NFFT)/L;
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);
figure
plot(t, s)
grid
xlabel('t')
ylabel('s(t)') figure
plot(Fv, abs(FTs(Iv))*2)
grid
xlabel('Frequency')
ylabel('Magnitude') % syms omega t
% s = sin(2*pi*t*50) * exp(-(t-0.3)^2 * 50)
%
% FTss(omega) = int(s*exp(1j*omega*t), t, -Inf, Inf)
%
% figure
% fplot(FTss, [0 100])
% grid
The numerical transform code should work with any ‘s’ function you care to use with it. Just be certain that the data are regularly (uniformly) sampled. A function (nufft) for non-uniformly sampled data is available as well.
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