Is it right this relationship?
$y(\omega)=A(\omega)\cdot e^{j \phi(\omega)}$ can be written as $y(\omega)=y(t)=A(\omega) \cdot \sin[\omega t + \phi(\omega)]$
Because I got several couples of amplitude and phases, each couple associated to a certain frequency, so that:
$\omega_1 \rightarrow (A_1,\phi_1)$
$\omega_2 \rightarrow (A_2,\phi_2)$
and so on.
Assuming that in a certain time instant, $t=1$, the frequency is equal to $\omega_1$, how can I build that signal in the time domain? Is it right to state:
$y(t_1) = y(\omega_1)=A_1 \cdot e^{j \phi_1}=A_1 \cdot \sin(\omega_1 t_1 + \phi_1)$
or not?