I did this:
points = {{-5, 0}, {-4.8, 3}, {-4.5, 1}, {-4.2, 1}, {-4,
3.5}, {-3.8, 0}, {-3.5, 6}, {-3.1, 0}, {-3, -5.5}, {-2.8,
0}, {-2.5, 6}, {-2.1, 0}, {-1.8, -2.5}, {-1.5, 0}, {-1.2,
5}, {-0.8, 0}, {-0.5, -8}, {-0.2, 0}, {0, 18}, {1/2,
0}, {2/3, -8}, {1, 0}, {4/3, 4}, {3/2, 0}, {1.6, -4}, {2,
3}, {2.5, -3}, {3, 3}, {3.2, -2}, {3.5, 2}, {3.8, -4}, {4.2,
0}, {4.5, 6}, {4.8, -5}, {5, 0.1}};
Formed a piecewise function:
f[t_] = draupnerfun[t_] :=
Piecewise[
Table[{points[[i, 2]], points[[i, 1]] > t}, {i,
Length[points]}], 0]
p0 = Plot[draupnerfun[t], {t, -5, 5}]
and did a Fourier transform:
dft2 = FourierTransform[draupnerfun[t], t, k];
Plot[Evaluate[Re[dft2]], {k, -4, 4}]
and got this
which means the Fourier transformed converged.
The Fourier transform issued by this command is:
However, when I tried to do this by using the Definition:
Integrate[f[t]/E^(I (k t)), {k, -Infinity, Infinity}]
I got:
"Integral of E^(-I k t) Null does not converge on {-[Infinity],[Infinity]}."
Then I did this on the interval [-5,5]:
Integrate[f[t]/E^(I (k t)), {k, -5, 5}]
and got:
2 Null Sin[5 t])/t
So what is:
FourierTransform[draupnerfun[t], t, k];
if it is not the integral in the definition or in the bounded domain?
Thanks
