KeyFingot
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I understand that one can define (where constants on forward and backward transform have to multiply to 1/2pi)
 g(k)=\dfrac{1}{2\pi}\int\limits_{-\infty}^{\infty}\!\!f(x)e^{-ikx}\,\mathrm{d}x

as the fourier transform of f(x), but what does it actually do? What is it used for?
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KeyFingot
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davros
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(Original post by KeyFingot)
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No offence, but why don't you just Google "use of Fourier Transform"?

There should be enough to keep you busy for months
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KeyFingot
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(Original post by davros)
No offence, but why don't you just Google "use of Fourier Transform"?

There should be enough to keep you busy for months
That's fair enough for what it can be used for, but how about what it actually does?

What does the function g(k) in general represent when compared to f(x)?
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davros
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(Original post by KeyFingot)
That's fair enough for what it can be used for, but how about what it actually does?

What does the function g(k) in general represent when compared to f(x)?
It's a long time since I've used these, but I think it's fair to say that the transformed function g(k) in general bears no resemblance to the original function f(x).

However, there are various fascinating formulae that link the two, such as the Fourier inversion formula, and also Rayleigh's formula which is the Fourier-transform equivalent of Parseval's formula for Fourier series if you've come across the latter.
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