Consider a continuous-time signal xc(t) with Fourier transform shown in Figure P4.21-1...

Consider a continuous-time signal x_c(t) with Fourier transform shown in Figure P4.21-1.

(a) A continuous-time signal x_r(t) is obtained through the process shown in Figure P4.21- 2. First, x_c(t) is multiplied by an impulse train of period T1 to produce the waveform x_s(t), i.e.,

Next, xs (t) is passed through a low pass filter with frequency response is shown in Figure P4.21-3. .

Determine the range of values for T1 for which xr (t) = xc(t). (b) Consider the system in Figure P4.21-4. The system in this case is the same as the one in part (a), except that the sampling period is now T2. The system is some continuous-time ideal LTI filter. We want xo(t) to be equal to xc(t) for all t , i.e., xo(t) = xc(t) for some choice of . Find all values of T2 for which xo(t) = xc(t) is possible. For the largest T2 you determined that would still allow recovery of xc(t), choose so that xo(t) = xc(t). Sketch .