Suppose that xc(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 xc(t) with sampling period T ; i.e., x[n] = xc(nT ).
(a) Show that φ[m], the autocorrelation sequence for x[n], is
(b) What is the relationship between the power density spectrum Pc(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
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