Which of these is correct for Fourier transform?

Asked Mar 17 '15 at 09:25

Active Mar 17 '15 at 12:18

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Which of these is a correct definition of Fourier transform?

$$\mathcal{F}(f(x))= \int\limits_{-\infty}^{\infty} f(x)\, e^{-i k x} \, \mathrm{d} x \ \ \ \ (1)$$ and$$\mathcal{F}(f(x))= \int\limits_{-\infty}^{\infty} f(x)\, e^{i k x} \, \mathrm{d} x\ \ \ \ (2)$$

I use form (1) with a negative exponent,but I see some people use form (2). I want to know which is the correct definition.

edited Mar 17 '15 at 12:18

Najib Idrissi

54,185

asked Mar 17 '15 at 09:25

user62498

3,556

The integral should be over the variable of f. dx and not dk. Also the result of the transform is a function of k. – mathreadler Mar 17 '15 at 09:27
It does not matter so much the sign of the exponent. It will only mirror the phase. But it is important that the result of the transformation is a function of k and that the integral is with respect to the function variable x. – mathreadler Mar 17 '15 at 09:29
@ ِDear mathreadler yes I am sorry – user62498 Mar 17 '15 at 09:39
1

Don't be sorry. Just focus on trying to learn. :) – mathreadler Mar 17 '15 at 09:40

Which of these is correct for Fourier transform?

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