The message signal m(t) = 10cos(1000t) frequency modulates the carrier c(t) = 10cos(2fct). The modulation index is 10. 1) Write an expression for the modulated signal u(t).
2) What is the power of the modulated signal.
3) Find the bandwidth of the modulated signal.

1) 10cos ( 2πfct + 10sin 2πfmt )

2) 50 watts

3) 1000 Hz

Explanation:

m(t) = 10cos(1000πt)

c(t) = 10cos(2πfct )

modulation index (  = 10

1) expression for modulated signal ( u(t) )

u(t) = Ac(cos 2πfct ) + A (cos 2πfct m(t) ) Am cos2πf mt

      = 10cos 2πfct + 100 cos 2πfct  cos2π500t

      = 10cos ( 2πfct + 10sin 2πfmt )

2) power of modulated signal

power of modulated signal  μ^2 / 2 ]

           = 10^2/2 ]

           = 50 watts

3) Bandwidth

B = 2fm  = 2 * 500 = 1000 Hz

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