Why are there so many different notation formats for the Fourier Transform?
Wikipedia defines it in this way for a function $x(t)$: $$\hat{f}(k) = \int_{-\infty}^{\infty}x(t)e^{-2\pi i kt}dt$$ However I also see the following
- $F(k)$
- $F(ik)$
- $F(2\pi ik)$
- $F_x(k)$
- $F[x(t)](k)$
- $F_t[x(t)](k)$
There are also many various combinations of the above I haven't mentioned (and also more if you consider angular frequency). The versions I understand the least are why you would ever include non-variables in the argument ($2\pi i$ for example).