Let $$g(t) = g_r(t) + j g_i(t)$$ be a complex signal with $g_r(t)$ and $g_i(t)$ real signals.
We can write the Fourier transform $$G(f) = G_r(f) + jG_i(f),$$ where $G_r(f)$, $G_i(f)$ and $G(f)$ are Fourier transforms of $g_r(t)$, $g_i(t)$ and $g(t)$, respectively and are complex functions in general.
How can I write $G_r(f)$ and $G_i(f)$ in terms of $G(f)$? Any proof along with the answer would be appreciated.