**Q1)** For a single sideband modulator performing multi-tone modulation, the message signal is 8 sin *ω*_{m}*(t)* + 4 cos *2ω*_{m}*t*, the carrier is cos *ω*_{c}*t* and *ω** _{c}* = 10

*ω*

*. Determine the time domain expressions for the upper sideband and the lower sideband versions of the SSB signal.*

_{m}**(4 points)**

**Q2) **The message signal input to a modulator is given by *A*_{m}*cos*(*2π×10*^{4}*t*). **(4 points)**

(a) If frequency modulation is performed with *k*_{f}* =5π* × 10^{4}, find the FM bandwidth when (i) *A** _{m}* = 2 and (ii)

*A*

*= 4.*

_{m}(b) If phase modulation is performed with *k** _{p}* = 2.25, find the PM bandwidth when

(i)

*A*

*= 2 and (ii)*

_{m}*A*

*= 4.*

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

Assume that Δ= 0.02*π*. **(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 *m*_{1}*(t)* and *m*_{2}*(t)*. The highest frequency of *m*_{1}*(t)* is 4 kHz, while that of *m*_{2}*(t)* is 3.2 kHz. Determine the minimum allowable sampling rate. **(4 points)**

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