X(t) is a wide sense stationary stochastic process with X = 0 and autocorrelation function

RX () = e5000| |

Observe Y(t) = X(t)+N(t), where N(t) is a wide sense stationary process with power spectral density function SN(f) = 105. X(t) and N(t) are mutually independent.

(a) What is the transfer function of the optimum linear filter for estimating X(t) given Y(t)?

(b) What is the mean square error of the optimum estimation filter?