# Newbie fourier transform question

Fourier Transform equations

Ultimately, I want to understand spatial data operated on by Fourier Transforms, what am I loooking at in a transformed image. I did some introduction at uni and understand unit circles, Euler's Formula and linear combinations.

So far I am stuck trying to understand the equations in the image and want to be sure. Is the frequency a constant value in the integral of the time equation, and is time a constant for the integral of the frequency equation? If so, that would mean any integration is for a specific frequency or time.

So when a signal is broken into component periodic signals, how does it "know" the range of frequencies/time to transform? Or am I no where near understanding this?

THanks.

$$X(\Omega) = \int_\mathbb{R} x(t) e^{-j\Omega t} \ dt$$
returns a function of $\Omega$. That should be treated as "fixed" in the integrand. Similar reasoning holds for the inverse transform.