Correct Answer - Option 3 : 3 kHz
Concept:
SSB (Single Side Band) modulation is a technique that allows only one sideband to pass saving bandwidth and power both.
Practically it is very difficult to pass only a single sideband.
Ex: If we consider a single-tone modulating signal as x(t) = cos ωmt, the SSB modulated wave with only the upper sideband will be represented as:
cos ((ωc + ωm)t) = cos ωc.cos ωmt – sin ωc.sin ωmt
and with lower sideband only will be represented as:
cos (ωc - ωm)t = cos ωct .cos ωmt + sin ωct. sin ωmt
where sin ωmt is the Hilbert transform of the original message signal x(t) = cos ωmt
Generalizing this for any signal m(t), we can say that the SSB modulated signal with only upper sideband will be:
m(t) cos ωct – m̂(t) sin ωct, (option 1 is the correct answer)
Similarly, we can say that the SSB modulated signal with only lower sideband will be:
m(t) cos ωct + m̂(t) sin ωct,
where m̂(t) is the Hilbert transform of m(t).
The generalized AM expression is represented as:
s(t) = Ac [1 + μa mn (t)] cos ωct
The RF bandwidth of an SSB-AM signal is also 3 kHz.
