Question

An SSB AM modulator with carrier signal of c(t) = 20 cos(600πt) is used to transmit the following message signal.

m(t) = 3 cos(40πt) + 7 sin(64πt)
Determine the expression for the upper-sideband signal. Sketch the amplitude spectrum of the uppersideband SSB signal showing both the amplitudes and the frequencies of all the transmitted components. Repeat the same analysis for the lower-sideband SSB signal.

Answer 1

To find the upper-sideband signal in SSB AM modulation, multiply the message signal with the carrier wave and take the Fourier transform. The amplitude spectrum of the upper-sideband SSB signal shows the amplitudes and frequencies of the transmitted components. The same analysis can be done for the lower-sideband SSB signal.

Step-by-step explanation:

In SSB AM modulation, the upper-sideband signal can be obtained by multiplying the message signal with the carrier wave and taking the Fourier transform.

To find the upper-sideband signal, we can use the formula:

m(t) * c(t) = ((3 cos(40πt) + 7 sin(64πt)) * 20 cos(600πt))

Expanding this expression, we get:

upper-sideband signal = 60 cos(40πt)cos(600πt) + 140 sin(64πt)cos(600πt)

The amplitude spectrum of the upper-sideband SSB signal would show the amplitudes of the individual components (60 and 140) and their corresponding frequencies (40π and 64π) in the Fourier transform graph.

Similarly, we can find the lower-sideband signal by multiplying the message signal with the carrier wave and taking the Fourier transform, but with a negative sign in the expression.

lower-sideband signal = -60 cos(40πt)cos(600πt) - 140 sin(64πt)cos(600πt)

The amplitude spectrum of the lower-sideband SSB signal would show the amplitudes of the individual components (-60 and -140) and their corresponding frequencies (40π and 64π) in the Fourier transform graph.