I know there's similar questions here, but I did not fully understand the answers I have read: in MATLAB I consider the complex envelope of an output signal:
y_low_out = A_low_out .* exp(1i*Phi_low_in) .* exp(1i*Phi_low_out);
Now, I want to recover a sinusoidal signal, what does y_out look like in terms of superpositions of sine-waves? My guess is:
y_out = A_low_out .* sin(2*pi*f_c*t + Phi_low_in + Phi_low_out)
But this is pure guessing. $f_c$ is the carrier frequency.
Some background to what I am trying to do: I consider an input signal:
x(t) = A_in .* sin(2*pi*(f_c+f1)*t + Theta1) + A_in .* sin(2*pi*(f_c+f2)*t + Theta2))
This input signal is converted to an equivalent lowpass signal (complex envelope) with amplitude A_low_in and phase Phi_low_in and sent through a nonlinearity which changes both amplitude and phase. The amplitude of my output signal (still complex envelope) is A_low_out, the phase change is Phi_low_out. This description refers to the code that I have written. I have determined A_low_in by taking the absolute value of the analytic signal of x. For some reason A_in and A_low_in are not the same. I figured A_low_in would be twice A_in, but it's not exactly (maybe numerical differences). Anyways, in the end I get the complex envelope y_low_out. And I want to convert it to y_out.