Consider the random process of Problem 7.3. (a) Find the time-average mean and the auto correlation function.

Question:

Consider the random process of Problem 7.3.
(a) Find the time-average mean and the auto correlation function.
(b) Find the ensemble-average mean and the auto correlation function.
(c) Is this process wide-sense stationary? Why or why not?


Data From Problem 7.3

A random process is composed of sample functions that are square waves, each with constant amplitude T0, and random delay Ï„ as sketched in Figure 7.15. The pdf of Ï„ is 

S 1/T,, |7| < To/2 0, f (t) = otherwise

Figure 7.15

X(t) - т To
(a) Sketch several typical sample functions.
(b) Write the first-order pdf for this random process at some arbitrary time t0. (Because of the random delay Ï„, the pdf is independent of t0. Also, it might be easier to deduce the cdf and differentiate it to get the pdf.)

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