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Unformatted text preview: THE STATE UNIVERSITY OF NEW JERSEY RUTGERS College of Engineering Department of Electrical and Computer Engineering 332:322 Principles of Communications Systems Spring 2004 Problem Set 9 Haykin: 1.1–1.10 1. Consider a random process X ( t ) defined by X ( t ) = sin (2 πf c t ) in which the frequency f c is a random variable uniformly distributed over the range [0 , W ] . Show that X ( t ) is nonstationary. Hint: Examine specific sample functions of the random process X ( t ) for the frequency f = W/ 2 , W/ 4 and W say. 2. Let X and Y be statistically independent Gaussian-distributed random variables each with zero mean and unit variance. Define the Gaussian process Z ( t ) = X cos (2 πt ) + Y sin (2 πt ) (a) Determine the joint probability density function of the random variables Z ( t 1 ) and Z ( t 2 ) obtained by observing Z ( t ) at times t 1 and t 2 respectively. (b) Is the process Z ( t ) stationary? Why?...
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- Spring '08
- Variance, Probability theory, Autocorrelation, probability density function