Computing difficult Fourier series numerically - software recommendation

Question

I need to compute some pretty complex Fourier series of function like this one:

$$ f(t) = \quad \begin{cases} 1+e^{-t}, & t\in [0;1)\\ 2, & t \in [1;3) \end{cases} $$

Rewritten to "one-line form:

$$ heaviside(x) * heaviside(1-x) * (1 + exp(-x)) + heaviside(x-1) * heaviside(3-x) $$

With period T=3.

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When I tried to compute it by WolframAlpha, I got just "Computing time exceeded" error - Wolfram.

Do you have any idea, how could I compute this series? As far as I know, MatLab/Octave doesn't have any function for this...

Answer 1

[Too long for a comment]

Here’s what Mathematica finds, with the function period scaled to $2\pi$.

f[t_]=Piecewise[{
  {1+E^(-(3/(2\[Pi]))Mod[t,2\[Pi]]),0<=Mod[t,2\[Pi]]<2/3 \[Pi]},
  {2,2/3 \[Pi]<=Mod[t,2\[Pi]]<2\[Pi]}
}]
s[t_]=FourierSeries[f[t],t,10]
Plot[{f[t],s[t]},{t,0,2\[Pi]}]

$2-\frac{1}{3 e}-\frac{i (-1+e) e^{3 i t-1}}{3 (-i+2 \pi )}+\frac{i (-1+e) e^{-3 i t-1}}{3 (i+2 \pi )}-\frac{i (-1+e) e^{6 i t-1}}{3 (-i+4 \pi )}+\frac{i (-1+e) e^{-6 i t-1}}{3 (i+4 \pi )}-\frac{i (-1+e) e^{9 i t-1}}{3 (-i+6 \pi )}+\frac{i (-1+e) e^{-9 i t-1}}{3 (i+6 \pi )}+\frac{e^{-2 i t} \left(9 e+3 i \sqrt{3} e+4 i \pi -4 \sqrt{3} \pi -4 i e \pi +4 \sqrt{3} e \pi \right)}{24 i e \pi +32 e \pi ^2}+\frac{e^{10 i t-1} \left(20 \pi \left(-i+\sqrt{3}\right)+e \left(-20 \pi \left(-i+\sqrt{3}\right)+3 \sqrt{3} i+9\right)\right)}{40 \pi (-3 i+20 \pi )}+\frac{e^{7 i t-1} \left(14 \pi \left(-i+\sqrt{3}\right)+e \left(-14 \pi \left(-i+\sqrt{3}\right)+3 \sqrt{3} i+9\right)\right)}{28 \pi (-3 i+14 \pi )}+\frac{e^{4 i t-1} \left(8 \pi \left(-i+\sqrt{3}\right)+e \left(-8 \pi \left(-i+\sqrt{3}\right)+3 \sqrt{3} i+9\right)\right)}{16 \pi (-3 i+8 \pi )}+\frac{e^{i t-1} \left(e \left(-2 \pi \left(-i+\sqrt{3}\right)+3 \sqrt{3} i+9\right)-4 (-1)^{5/6} \pi \right)}{4 \pi (-3 i+2 \pi )}+\frac{e^{-5 i t-1} \left(e \left(10 \pi \left(-i+\sqrt{3}\right)+3 \sqrt{3} i+9\right)-10 \left(-i+\sqrt{3}\right) \pi \right)}{20 \pi (3 i+10 \pi )}+\frac{e^{-8 i t-1} \left(e \left(16 \pi \left(-i+\sqrt{3}\right)+3 \sqrt{3} i+9\right)-16 \left(-i+\sqrt{3}\right) \pi \right)}{32 \pi (3 i+16 \pi )}+\frac{e^{-i t-1} \left(4 \sqrt[6]{-1} \pi -e \left(2 \pi \left(i+\sqrt{3}\right)+3 \sqrt{3} i-9\right)\right)}{4 \pi (3 i+2 \pi )}+\frac{e^{2 i t-1} \left(e \left(4 \pi \left(i+\sqrt{3}\right)-3 i \sqrt{3}+9\right)-4 \left(i+\sqrt{3}\right) \pi \right)}{8 \pi (-3 i+4 \pi )}+\frac{e^{-4 i t-1} \left(8 \left(i+\sqrt{3}\right) \pi -e \left(8 \pi \left(i+\sqrt{3}\right)+3 \sqrt{3} i-9\right)\right)}{16 \pi (3 i+8 \pi )}+\frac{e^{5 i t-1} \left(e \left(10 \pi \left(i+\sqrt{3}\right)-3 i \sqrt{3}+9\right)-10 \left(i+\sqrt{3}\right) \pi \right)}{20 \pi (-3 i+10 \pi )}+\frac{e^{-7 i t-1} \left(14 \left(i+\sqrt{3}\right) \pi -e \left(14 \pi \left(i+\sqrt{3}\right)+3 \sqrt{3} i-9\right)\right)}{28 \pi (3 i+14 \pi )}+\frac{e^{8 i t-1} \left(e \left(16 \pi \left(i+\sqrt{3}\right)-3 i \sqrt{3}+9\right)-16 \left(i+\sqrt{3}\right) \pi \right)}{32 \pi (-3 i+16 \pi )}+\frac{e^{-10 i t-1} \left(20 \left(i+\sqrt{3}\right) \pi -e \left(20 \pi \left(i+\sqrt{3}\right)+3 \sqrt{3} i-9\right)\right)}{40 \pi (3 i+20 \pi )}$