I'm extracting a portion of my notes which I believe I might have copied wrongly.
Given this equation:
$$\frac{G(\omega)}{2ic\omega} [e^{ic\omega t}-e^{-icwt}]$$
I want to find the Fouerir transform of the above. I believe it involves the Fourier transform of the signum function. The Signum function is:
$$sgn(x) = \left\{\begin{matrix} 1 ,&x>0 \\ 0,&x=0 \\ -1, &x<0 \end{matrix}\right.$$ On my notes it says the Fourier transform of sgn(x) to be $$\frac{1}{\pi i\omega}$$ (is this the correct?)
Secondly, how do I apply the fourier transform to the above equation?
I'm pretty lost so any help would be good.