In this problem, we develop an alternative derivation for the mean function of the shot noise process
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Where the are the arrival times of a Poisson process with arrival rate, λ, and h (t) is an arbitrary pulse shape which we take to be causal. That is, h (t) = 0 for t
(a) Use the results of Exercise 8.40 to justify that
Where the Xi are a sequence of IID random variables uniformly distributed over [0, t].
(b) Show that the expectation in part (a) reduces to
(c) Finally, average over the Poisson distribution of the number of arrivals to show that
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Probability and Random Processes With Applications to Signal Processing and Communications
ISBN: 978-0123869814
2nd edition
Authors: Scott Miller, Donald Childers
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