An AM signal is written as
xc(t) = Ac(1+µx(t))cos(2pifct)
where fc is the carrier frequency, Ac is the carrier amplitude, µ is the modulation index, and x(t) is the baseband message signal. We assume
that x(t) has absolute bandwidth W << fc, and that its amplitude has been normalized so that |x(t)| <= 1.
If x(t) is a cosine of amplitude 1 and frequency fm << fc:
• Obtain an expression for the amplitude spectrum X c(f) of the AM signal xc(t).
• Determine the power in the carrier and in the sidebands. Express the powers in units of dBm into a 50 ohm load. (Remember that
the spectrum analyzer input impedance is 50 ohm)
• Determine the ratio of the power in the sidebands to the power in the carrier