Sorry if it's a bother but do you know how to compute Fourier transforms? I'm trying to learn how, I've seen the Wikipedia article and saw this:

for every real number ξ.

Does this mean that if I put in some function of x, such as sin(x), I'll get f(ξ) where ξ is a real number? Not sure, I'll post my working in a second. Sorry if I sound stupid...