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CUE4815Spring07_PROBLEMSET4

# CUE4815Spring07_PROBLEMSET4 - k k for k=0 1 2 … ∞ x(t A...

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RANDOM SIGNALS AND NOISE ELEN E4815 COLUMBIA UNIVERSITY SPRING SEMESTER 2007 Problem Set # 4 Due Date: 21 February 2007 Problems #1 and 2 Problems 8.11 and 8.20 from Miller’s Book. Problem #3 Consider the so-called random telegraph signal, x(t) (shown below). In this signal, which started in time at - and will continue to + , the voltage flips back and forth, between +A volts and –A volts, in the following manner. The switching times, are dictated by a Poisson distribution, i.e., the probability of “k” flips in τ seconds is given by the Poisson distribution function Prob {of “k” flips in τ seconds}= [e - λτ { λτ

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Unformatted text preview: } k ]/ k! for k=0, 1, 2, …. ∞ . x(t) A t -A “a flipping instant” a) Find the autocorrelation function, E{x(t+ τ ) x(t)} of random process, x(t), and show that it is only a function of τ . b) Show that the E{x(t)} is just a constant. Therefore, this process is WSS. c) Find and draw the Power Spectral Density, P x (f), of the random process. d) Repeat the parts above if the voltage flips between +A and 0 (not –A) Hint: If you are having a problem, look at pp.376-377, in Miller and Childers. Problem #4 and 5 Problems -1.5 and 1.8 in Chapter 1 of Haykin’s Book (which may be found in the library)....
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CUE4815Spring07_PROBLEMSET4 - k k for k=0 1 2 … ∞ x(t A...

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