(Solved):   3) The block diagram of the modulator circuit of a TV station transmitter, depicted in Fig ...

 

3) The block diagram of the modulator circuit of a TV station transmitter, depicted in Figure \( 3(a) \), in which the video signal \( x_{G}(t) \) is transmitted by \( \mathrm{VSB} \). \( \mathrm{C} \) modulation and the audio signal \( x_{S}(t) \) is by \( \mathrm{FM} \) modulation. VSB filter, its passbas (b). \( { }^{2} \) idth is \( W_{T}=1 \mathrm{MHz} \), its impulse responcy deviation (drift) is \( \Delta f=150 \mathrm{kHz} \). For the a) Write the time-domain expression of \( x_{c}(t) \) (It is not required to find the signals \( x_{G}(t) \) and \( \left.x_{S}(t)\right) \). b) Plot the frequency spectrum of \( x_{c}(t) \) if the frequency spectra \( X_{G}(f)=\overparen{f}\left\{x_{G}(t)\right\} \) and \( X_{S}(f)=\mathbb{G}\left\{x_{S}(t)\right\} \) are given in Figure 3(c). Determine the bandwidth of the VSB+C and FM modulated signals (Carson rule should be used to determine the bandwidth of FM modulated signals). How much bandwidth should be given to this TV station if a total guard band of \( 1 \mathrm{MHz} \) is left so that TV signals do not interfere with other TV signals? Figure 3(c) c) Suppose that the superheterodyne technique is used in TV receiver such that it can receive the broadcast signals of this TV station. Draw the block diagram of the TV receiver's demodulator circuit where the intermediate frequency is \( f_{I F G}=39 \mathrm{MHz} \) for video signals and \( f_{I F S}=33 \mathrm{MHz} \) for audio signals. Brief explain how demodulation takes place.