An AM signal is written as xc(t) = Ac (1+ µx(t))cos(2pi*fc*t) 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: 2)
• 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) 3)Obtain numerical values in Item 2 if fm = 15 kHz, µ = 1/2, and the carrier amplitude and frequency are Ac = 1 and fc = 300 kHz 4)Repeat Item 2 for a message x(t) which is a square wave of amplitude 1, zero dc level, 50% duty cycle, and fundamental frequency fm 5)Obtain numerical values in Item 4 if fm = 15 kHz, µ = 1/2, and the carrier amplitude and frequency are Ac = 1 and fc = 300 kHz.