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What is the Fourier Function of Matlab doing?

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Hidden in the Matlab basic functions I discovered
existst. This seems useful I thought, because It applies the fourier-transform to the function f by calculating the complex integral.
But how can I take use of that? I thought, by doing the transform, I can simply plot it:
syms x
FT = fourier(x^2)
isn't doing much. Is there a misunderstanding at the root?

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Walter Roberson
Walter Roberson il 15 Gen 2021
syms x w
FT(w) = fourier(x^2, x, w)
FT(w) = 
FT(-1), FT(0), FT(1)
ans = 
ans = 
ans = 
The empty plot is to be expected as the value is 0 everywhere exact at w = 0 exactly, where it is -infinity .
  2 Commenti
Niklas Kurz
Niklas Kurz il 16 Gen 2021
Well, this isn't really helping me. I thought the Fourier-Transform depicts all koefficients of the trigonometric series in order that I can plot the combination.
Walter Roberson
Walter Roberson il 16 Gen 2021
No, that is not correct. The fourier transform is an infinite integral
The Fourier Transform is the infinite case of the Fourier Series
With the fourier transform being an infinite integral, there are some cases where the value of the entire integral is known; this happens to be one of them.

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