3. In addition to demodulating angle modulated signals, the PLL is well-known to provide phase- coherent demodulation in DSB-SC and SSB-SCAM systems by accomplishing carrier-phase estimation. Accordingly, consider the synchronous demodulation of a DSB-SC signal. The received noise corrupted signal at the input to the demodulator is given by: r(t)=u(t) + n(t)= Acm(t) cos(21fc t + c(t))+ n(t). a. Assuming that the received signal r(t) has a zero mean, since the message signal m(t) is zero mean; i.e., m(t) contains no dc component. Consequently, the average power at the output of a narrowband filter tuned to the carrier frequencyf is zero. How can you extract a carrier-signal component directly from the received signal ? Sketch the block diagram of the system for carrier- phase estimation, and mathematically explain the acquisition of carrier-signal component. (5 points). Explain the operation of a PLL in acquiring the phase of a carrier signal component. From which point in PLL the phase coherent carrier is taken out? Is it the same point from which demodulated signal taken in angle demodulation ? (5 points). c. Why the output of VCO is a sinus signal, whereas the incoming signal is expressed as a cosinus signal ? What property of trigonometry makes it possible to linearize the model of a PLL ? (5 points). 3. In addition to demodulating angle modulated signals, the PLL is well-known to provide phase- coherent demodulation in DSB-SC and SSB-SCAM systems by accomplishing carrier-phase estimation. Accordingly, consider the synchronous demodulation of a DSB-SC signal. The received noise corrupted signal at the input to the demodulator is given by: r(t)=u(t) + n(t)= Acm(t) cos(21fc t + c(t))+ n(t). a. Assuming that the received signal r(t) has a zero mean, since the message signal m(t) is zero mean; i.e., m(t) contains no dc component. Consequently, the average power at the output of a narrowband filter tuned to the carrier frequencyf is zero. How can you extract a carrier-signal component directly from the received signal ? Sketch the block diagram of the system for carrier- phase estimation, and mathematically explain the acquisition of carrier-signal component. (5 points). Explain the operation of a PLL in acquiring the phase of a carrier signal component. From which point in PLL the phase coherent carrier is taken out? Is it the same point from which demodulated signal taken in angle demodulation ? (5 points). c. Why the output of VCO is a sinus signal, whereas the incoming signal is expressed as a cosinus signal ? What property of trigonometry makes it possible to linearize the model of a PLL ? (5 points)