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A modulated signal is given by,
s(t) = m1(t) cos (2 π fct) + m2(t) sin (2 π fct)
where the baseband signal m1(t) and m2(t) have bandwidths of 10 kHz and 15 kHz respectively. The bandwidth of the modulated signal, in kHz, is
  • a)
    10
  • b)
    15
  • c)
    25
  • d)
    30
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A modulated signal is given by,s(t) = m1(t) cos (2 fct) + m2(t) sin (2...
Given:
s(t) = m1(t) cos (2 fct) m2(t) sin (2 fct)
Bandwidth of m1(t) = 10 kHz
Bandwidth of m2(t) = 15 kHz

To find:
Bandwidth of modulated signal s(t)

Solution:

The bandwidth of a modulated signal is given by the sum of the bandwidths of the message signal and the carrier signal.

The message signal m1(t) is being multiplied by the carrier signal cos(2fct), so the resulting signal has a bandwidth of 10 kHz centered around the carrier frequency fc.

Similarly, the message signal m2(t) is being multiplied by the carrier signal sin(2fct), so the resulting signal has a bandwidth of 15 kHz centered around the carrier frequency fc.

The modulated signal s(t) is the sum of these two signals, so its bandwidth is the sum of the bandwidths of the two message signals and the bandwidth of the carrier signal.

Bandwidth of carrier signal = fc

Therefore, the bandwidth of s(t) is:

Bandwidth of s(t) = 10 kHz + 15 kHz + fc

Since the carrier frequency is not given, we can assume a typical value of 100 kHz.

Bandwidth of s(t) = 10 kHz + 15 kHz + 100 kHz = 125 kHz

Therefore, the correct answer is option D, 30 kHz.
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A modulated signal is given by,s(t) = m1(t) cos (2 fct) + m2(t) sin (2 fct)where the baseband signal m1(t) and m2(t) have bandwidths of 10 kHz and 15 kHz respectively. The bandwidth of the modulated signal, in kHz, isa)10b)15c)25d)30Correct answer is option 'D'. Can you explain this answer?
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