# [SciPy-user] Fourier series

Ivo Maljevic ivo.maljevic@gmail....
Wed Oct 22 09:05:53 CDT 2008

```I think if you spent some time in deriving formulas it should be possible to
find it:

1) Since the function f(t) is periodic, its spectrum is discrete anyway, so
FFT will do the job, provided that you sample the frequency at multiple of
harmonics.

2) DFT coefficients are complex, but similar to c_n complex coefficients for
the fourier series, there is a relationship:
c_n = a_n -j*b_n, n > 0
c_n = a_n+j*b_n, n < 0

So, for positive m: a_m = 0.5*(c_m + c_{-m}), and similar approach goes for
b_m.

Sorry I cannot give you more info at this time. Hopefully this sketchy
approach will give you some ideas.

Ivo

2008/10/22 Nils Wagner <nwagner@iam.uni-stuttgart.de>

> Hi all,
>
> Is there a function in scipy to compute the Fourier
> coefficients
> a_0, a_1, b_1, a_2, b_2 of a periodic function f(t)=f(t+T)
>
> http://en.wikipedia.org/wiki/Fourier_series
>
> An example would be appreciated.
>
> Nils
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