What is the Fourier Function of Matlab doing?

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Niklas Kurz
Niklas Kurz 2021-1-15
评论： Walter Roberson 2021-1-16
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?

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Walter Roberson
Walter Roberson 2021-1-15
Ran in:
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 .
  2 个评论
Niklas Kurz
Niklas Kurz 2021-1-16
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 2021-1-16
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.

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