What is the Fourier Function of Matlab doing?

Hidden in the Matlab basic functions I discovered

fourier(f)

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)
fplot(FT)

isn't doing much. Is there a misunderstanding at the root?

Answer 1

[Walter Roberson]

https://math.stackexchange.com/questions/1707452/what-is-the-fourier-transform-of-fx-x2

syms x w
FT(w) = fourier(x^2, x, w)

FT(w) = 

FT(-1), FT(0), FT(1)

ans = 

0

ans = 

ans = 

0

fplot(FT)

The empty plot is to be expected as the value is 0 everywhere exact at w = 0 exactly, where it is -infinity .

[Niklas Kurz]

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]

No, that is not correct. The fourier transform is an infinite integral https://en.wikipedia.org/wiki/Fourier_transform#Definition

The Fourier Transform is the infinite case of the Fourier Series https://en.wikipedia.org/wiki/Fourier_Series#Definition

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.

[Guillermo Aldana]

There are at least 3 defintions of the Fourier Transform - Physic, math and engineering use slighlty different versions, some even with a 180 phase shift in frequency - which definition does matlab use?

[Paul]

See the More About section of the fourier doc page for the default parameterization of the Fourier transform. See sympref for how to specify parameters that aren't the defaults.