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Question

A modulated signal Cm(t) has the form Cm(t)=30sin300πt+10(cos200πtcos400πt). The carrier frequency fc the modulating frequency (message frequency) fω and the modulation index μ are respectively given by

A
fc=200Hz;fω=50Hz;μ=12
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B
fc=150Hz;fω=50Hz;μ=23
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C
fc=150Hz;fω=30Hz;μ=13
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D
fc=200Hz;fω=30Hz;μ=12
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Solution

The correct option is D fc=150Hz;fω=50Hz;μ=23
Amplitude modulated wave is represented as:
y(t)=Asin(2πfct)+Aμsin(2πfct)sin(2πfwt)
=Asin(2πfct)+Aμ2[cos(2π(fcfw)t)cos(2π(fc+fw)t)]

Comparing this with the given equation gives:
2πfc=300π,fc=150 Hz
2π(fcfw)=200π,fw=50 Hz
A=30
Aμ/2=10,μ=2/3

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