ps10-PulseMod - 6.450 Principles of Digital Communication...

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Unformatted text preview: 6.450 Principles of Digital Communication Wednesday, November 7, 2002 MIT, Fall 2002 Handout #35 Due: Wednesday, November 14, 2001 Problem Set 10 Problem 10.1 The purpose of this problem is to show that if { N j ; j Z } is a sequence of Gaussian rvs N (0 , 2 ), then the sampling theorem expansion N ( t ) = j N j sinc( t- jT ) is a stationary random process. (a) Suppose that an L 2 function x ( t ) is baseband limited to 1 / (2 T ) for some T > 0 and is the inverse Fourier transform of x ( f ). Show that for any fixed , x ( t- ) can be expressed as x ( t- ) = X j Z x ( jT- )sinc t- jT T (b) Show that sinc t- T = X j Z sinc - jT T sinc t- jT T (c) Consider the stochastic process N ( t ) = X j Z N j sinc t- jT T where { N j ; j Z } is a set of iid N (0 , 2 ) rvs. Find K N ( t, ) = E [ N ( t ) N ( )]. (d) Show that { N ( t ) } is a stationary Gaussian random process and find the covariance function K N ( t- ) = K N ( t, ). Note that the sample functions of)....
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This note was uploaded on 10/07/2009 for the course ENSC 5210 taught by Professor Daniellee during the Spring '08 term at Simon Fraser.

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ps10-PulseMod - 6.450 Principles of Digital Communication...

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