Consider the sampling of a sinc signal and related signals.

(a) For the signal x(t)=sin(t)/t, find its magnitude spectrum |X(Ω)|and determine if this signal is band-limited or not.

(b) What would be the sampling period Tsyou would use for sampling x(t) without aliasing?

(c) For a signal y(t) = x²(t) what sampling frequency f_s would you use to sample it without aliasing? How does this frequency relate to the sampling frequency used to sample x(t)?

(d) Find the sampling period T_s to sample x(t) so that the sampled signal x_s(0) = 1 otherwise x(nT_s) = 0 for n ≠ 0.