Suppose that xc(t) is a real, continuous-time stationary random signal with autocorrelat...

Suppose that x_c(t) is a real, continuous-time stationary random signal with autocorrelation function

and power density spectrum

Consider a discrete-time stationary random signal x[n] that is obtained by sampling x_c(t) with sampling period T ; i.e., x[n] = x_c(nT ).

(a) Show that φ[m], the autocorrelation sequence for x[n], is

(b) What is the relationship between the power density spectrum P_c(Ω) for the continuous-time random signal and the power density spectrum P(ω) for the discrete-time-random signal?

(c) What condition is necessary such that