Unformatted text preview: Consider the random process W ( t ) = Xcos (2 πf t ) + Y sin (2 πf t ) where X and Y are uncorrelated random variables each with expected value and variance σ 2 . Find the autocorrelation R W ( t, τ ) . Is W ( t ) wide sense stationary? Problem 5 X ( t ) is a wide sense stationary random process with average power equal to 1 . Let Θ denote a random variable with uniform distribution over [0 , 2 π ] . such that X ( t ) and Θ are independent. a) What is E [ X 2 ( t )] ? b) What is E [ cos (2 πf c t + Θ)] ? c) Let Y ( t ) = X ( t ) cos (2 πf c t + Θ) . What is E [ Y ( t )] ? d) What is the average power of Y ( t ) ?...
View Full Document
- Spring '07
- Probability, Probability theory, Stochastic process, stationary random process, 351K