LP to BP transformation steps

Question

Considering the following problem, What i know to convert from LP signal to BP signal is to:

1. Draw the FD of the LP equation
2. From it I can draw the FD for BP
3. From this graph I can deduce the equation of the BP signal.

My problem here is that the equation has an Imaginary value, so how can i plot this equation and how can i deduce the graph of BP signal from it؟ because i searched and i found results about Hilbert transform and imaginary odd symmetry but i didn't figure that out.

Answer 1

HINT:

Just multiply the complex baseband signal with a complex carrier $e^{j2\pi f_ct}$, and take the real part to obtain the corresponding real-valued band pass signal. You can sketch either the magnitude or the real and imaginary parts separately.