Consider the system shown in Figure P4.35-1. For parts (a) and (b) only, Xc(jΩ) = 0 for...

Consider the system shown in Figure P4.35-1. For parts (a) and (b) only, X_c(jΩ) = 0 for |Ω| > 2π ×10³ and H(e^jω) is as shown in Figure P4.35-2 (and of course periodically repeats).

(a) Determine the most general condition on T, if any, so that the overall continuous-time system from x_c(t) to y_c(t) is LTI.

(b) Sketch and clearly label the overall equivalent continuous-time frequency response H_eff(jΩ) that results when the condition determined in (a) holds.

(c) For this part only assume that X_c(jΩ) in Figure P4.35-1 is bandlimited to avoid aliasing, i.e., . For a general sampling period T, we would like to choose the system H(e^jω) in Figure P4.35-1 so that the overall continuous-time system from x_c(t) to y_c(t) is LTI for any input x_c(t) bandlimited as above. Determine the most general conditions on H(e^jω), if any, so that the overall CT system is LTI. Assuming that these conditions hold, also specify in terms of H(e^jω) the overall equivalent continuous-time frequency response H_eff(jΩ).