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solve the Communication System problem

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Q1) For a single sideband modulator performing multi-tone modulation, the message signal is 8 sin ωm(t) + 4 cos mt, the carrier is cos ωct and ωc = 10ωm. Determine the time domain expressions for the upper sideband and the lower sideband versions of the SSB signal. (4 points)

Q2) The message signal input to a modulator is given by Am cos(2π×104t). (4 points)

(a) If frequency modulation is performed with kf =5π × 104, find the FM bandwidth when (i) Am = 2 and (ii) Am = 4.

(b) If phase modulation is performed with kp = 2.25, find the PM bandwidth when
(i) Am = 2 and (ii) Am = 4.

Q3) Given that a delta modulation has m(t) = 3cos40πt + 4cos60πt, calculate the minimum sampling frequency required to prevent slope overload.

Assume that Δ= 0.02π. (4 points)

Q4) Twenty baseband channels, each band-limited to 2.4 kHz, are sampled and multiplexed at a rate of 6 kHz. What is the required bandwidth for transmission if the multiplexed samples use a PCM system?(4 points)

Q5) Time-division multiplexing is used to transmit two signals m1(t) and m2(t). The highest frequency of m1(t) is 4 kHz, while that of m2(t) is 3.2 kHz. Determine the minimum allowable sampling rate. (4 points)

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