Response to the following problem:
A discrete-time stochastic process X(n) ≡ X(nT ) is obtained by periodic sampling of a continuous-time zero-mean stationary process X(t), where T is the sampling interval; i.e., fs = 1/T is the sampling rate.
a. Determine the relationship between the autocorrelation function of X(t) and the autocorrelation sequence of X(n).
b. Express the power density spectrum of X(n) in terms of the power density spectrum of the process X(t).
c. Determine the conditions under which the power density spectrum of X(n) is equal to the power density spectrum of X(t).