ps3 - EE 805, Random Processes and Linear Systems Jan. 27,...

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Unformatted text preview: EE 805, Random Processes and Linear Systems Jan. 27, 2012 OSU, Winter 2012 Due: Feb. 6, 2012 Problem Set 3 Problem 1 Consider the random process X ( t ) = p sin 2 f t + B [ n ] 2 , nT 6 t < ( n + 1) T, where p and f are known constants and B [ n ] is an iid Bernoulli random sequence taking on values 1, each with probability 1/2, and- < n < . Usually, f T is an integer, and we will assume so here. (a) Sketch a sample path X ( t ). (b) Find m X ( t ) and C XX ( s,t ). (c) Is the process sss? wss? Explain. Problem 2 Let W ( t ) (for t > 0) be a standard Wiener process with variance 2 t . (a) Find two times t 1 and t 2 for which the two r.v.s W ( t i ) ,W (2) have a correlation coefficient = 0 . 8 for both i = 1 and 2. (b) For arbitrary t and > 0, can two such times t 1 and t 2 be found for which the correlation coefficient between W ( t ) and W ( t i ) is , for both i = 1 and 2? Explain. What if < 0?...
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This note was uploaded on 03/18/2012 for the course ECE 805 taught by Professor Eryilmaz during the Spring '12 term at Ohio State.

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ps3 - EE 805, Random Processes and Linear Systems Jan. 27,...

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