I have a function
f(t) = 2t(H(t)-H(t-2))
and I want to transform it with fourier transformation, but I'm not sure how heaviside acts at least when there are no given limits to the function.
I do know that I'll get there using
$$f_{transform} = \int_{-\infty}^\infty2t(H(t)-H(t-2))e^{-j\omega t}dt $$
but beyond that, I am not sure how to do it by hand.