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I have a periodic function of period T and would like to know how to obtain the list of the Fourier coefficients. I tried using fft module from numpy but it seems more dedicated to Fourier transforms than series. Maybe it a lack of mathematical knowledge, but I can't see how to calculate the Fourier coefficients from fft.
Help and/or examples appreciated.
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So this is what we do: Take our target function, multiply it by sine (or cosine) and integrate (find the area) Do that for n=0, n=1, etc to calculate each coefficient. And after we calculate all coefficients, we put them into the series formula above.
The coefficients are returned as a python list: [a0/2,An,Bn]. a0/2 is the first Fourier coefficient and is a scalar. An and Bn are numpy 1d arrays of size n, which store the coefficients of cosine and sine terms respectively. To calculate these coefficients I perform integration using the script.
In the end, the most simple thing (calculating the coefficient with a riemann sum) was the most portable/efficient/robust way to solve my problem:
import numpy as np def cn(n): c = y*np.exp(-1j*2*n*np.pi*time/period) return c.sum()/c.size def f(x, Nh): f = np.array([2*cn(i)*np.exp(1j*2*i*np.pi*x/period) for i in range(1,Nh+1)]) return f.sum() y2 = np.array([f(t,50).real for t in time]) plot(time, y) plot(time, y2) gives me: 
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