Problem 3.4: In the block diagram shown below, a signal x(t) is multiplied by a Dirac delta train with a period Ts. The product of the two signals is then passed through an Ideal Low Pass Filter (ILPF) with cutoff frequency fcutoff and gain A. The output signal is denoted as z(t).
(a) If x(t) = 50sinc^2(50t) and Ts = 0.01, how should fcutoff and A be selected such that z(t) = x(t)?
(b) Now, set x(t) = 50sinc^2(50t), Ts = 0.005, and replace the Ideal Low Pass Filter with an Ideal Band Pass Filter (IBPF) with lower and upper cutoff frequencies 100 and 300 Hz, respectively. Choose A at your convenience. What will be the output z(t) for your value of A?
Show your work.