I feel like I keep getting confused about amplitudes when talking about signal processing. Maybe someone can help clear my confusion. Let's say I have a simple sinusoid:
$f(t)=A \sin(\omega_0 t)$.
The amplitude of this sinusoid is $A$ (which seems very obvious). But if I do a Fourier transform, $F(\omega)$ of $f(t)$ and then plot $|F(\omega) | $, I get a spike at $\omega_0$ and zeros elsewhere. $|F(\omega)|$ is called the "amplitude spectrum".
Does the amplitude spectrum have any relation to the amplitude, $A$?
Any help is appreciated.