Consider a continuous-time random process xc(t) with a bandlimited power density spectru...

Consider a continuous-time random process xc(t) with a bandlimited power density spectrum P_xcxc(Ω) as depicted in Figure P4.54-1. Suppose that we sample x_c(t) to obtain the discrete-time random process x[n] = x_c(nT ).

(a) What is the autocorrelation sequence of the discrete-time random process?

(b) For the continuous-time power density spectrum in Figure P4.54-1, how should T be chosen so that the discrete-time process is white, i.e., so that the power spectrum is constant for all ω?

(c) If the continuous-time power density spectrum is as shown in Figure P4.54-2, how should T be chosen so that the discrete-time process is white?

(d) What is the general requirement on the continuous-time process and the sampling period such that the discrete-time process is white?