1. ## Fourier transforms

How is it possible to recover $u(x)$ given the its fourier transform $v(\omega)$ and the inverse transform? by using the definition?

$v(\omega) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{-iwx}{u(x)}{dx}$

$u(x) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{iwx}{v(\omega)}{d\omega}$

is there some sort of change of variables that needs to be done?

Thanks

2. Originally Posted by bchanyi
How is it possible to recover $u(x)$ given the its fourier transform $v(\omega)$ and the inverse transform? by using the definition?

$v(\omega) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{-iwx}{u(x)}{dx}$

$u(x) =\frac{1}{(2\pi)^{1/2}}\int_{-\infty}^{\infty}e^{iwx}{v(\omega)}{d\omega}$

is there some sort of change of variables that needs to be done?

Thanks
I don't understand your question. You give the transform pair which tells
you how to find the FT of a function and how to recover the original function
from the transform (at least for functions for which these integrals have
meaning).

RonL

3. how do you sub v(w) into u(x) to recover u(x) back so that u(x)= u(x) to prove that that is the inversion formula. how can you do that? what manipulation are you suppose to do?