For a message signal m(t) = cos(2fmt) and carrier of frequency fC,which of the following represents a single side band (SSB) signala)cos (2fmt) cos(2fct)b)cos(2fct)c)cos [2(fc + fm)t]d)[1 + cos(2fmt)3cos(27fct) Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Explanation:

Single sideband (SSB) modulation is a type of amplitude modulation (AM) in which one of the sidebands is removed, leaving only the carrier and the other sideband. SSB signals are widely used in radio communication and broadcasting because they occupy less bandwidth than AM signals.

Given signal m(t) = cos(2fmt) and carrier of frequency fC, the SSB signal can be obtained as follows:

1. Amplitude modulation:

The message signal is used to modulate the amplitude of the carrier signal. The modulated signal can be represented as:

s(t) = m(t)cos(2πfCt)

where s(t) is the modulated signal, m(t) is the message signal, and fC is the carrier frequency.

2. Frequency shifting:

The modulated signal is shifted in frequency to remove one of the sidebands. This can be done using a frequency mixer. The mixer multiplies the modulated signal with a local oscillator signal of frequency fC + fm, where fm is the frequency of the message signal.

The mixer output can be represented as:

s'(t) = s(t)cos(2π(fC + fm)t)

= m(t)cos(2πfCt)cos(2πfmt) - m(t)sin(2πfCt)sin(2πfmt)

= 1/2m(t)cos(2π(fC - fm)t) + 1/2m(t)cos(2π(fC + fm)t)

where s'(t) is the output of the mixer, and the last step follows from the trigonometric identity cos(a+b) = cos(a)cos(b) - sin(a)sin(b).

3. Filtering:

The mixer output is filtered to remove the unwanted sideband. This can be done using a bandpass filter that passes only the desired sideband.

The filtered output can be represented as:

s''(t) = 1/2m(t)cos(2π(fC - fm)t)

or

s''(t) = 1/2m(t)cos(2π(fC + fm)t)

This is the desired SSB signal.

Answer: Option C (cos [2(fc - fm)t] or cos [2(fc + fm)t])

Answer

In single sideband signal,
since we are considering only one side of the band of frequency therefore for from one side and fm from other side will be added as a common cos signal
hence c .

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