6. (20 points) X (t) is a wide sense stationary process with zero mean and autocorrelation RX (t) = e− a | t | with a = p. We observe Y (t) = X (t) + N (t) where N (t) is a white Gaussian noise process with N0 = 10−5 . X (t) and N (t) are independent. (a) What is the transfer function of the optimum filter for estimat- ing X (t) given Y (t)? (b) What is the mean square error of the optimum filter estimate?

image 56 - 6. (20 points) X (t) is a wide sense stationary process with zero mean and autocorrelation RX (t) = e− a | t | with a = p. We observe Y (t) = X (t) + N (t) where N (t) is a white Gaussian noise process with N0 = 10−5 . X (t) and N (t) are independent. (a) What is the transfer function of the optimum filter for estimat- ing X (t) given Y (t)? (b) What is the mean square error of the optimum filter estimate?

This content is for Premium members only.
sign up for premium and access unlimited solutions for a month at just 5$(not renewed automatically)


images - 6. (20 points) X (t) is a wide sense stationary process with zero mean and autocorrelation RX (t) = e− a | t | with a = p. We observe Y (t) = X (t) + N (t) where N (t) is a white Gaussian noise process with N0 = 10−5 . X (t) and N (t) are independent. (a) What is the transfer function of the optimum filter for estimat- ing X (t) given Y (t)? (b) What is the mean square error of the optimum filter estimate?

already a member please login


7   +   1   =