Assignment:
A white Gaussian noise process X(t) with power spectral density (PSD) N0/2=0.1 is input to an LTI filter with a transfer function H(f) given by
The output is denoted Y(t).
(1) Find the autocorrelation function RX(t) of X(t).
(2) Find E[Y(t)].
(3) Find the PSD of Y(t).
(4) Determine a W such that E[Y2(t)] = 10.
(5) Find the first-order PDF of Y(t), i.e., fY(t)(y), when E[Y2(t)] = 10.
(6) Find the probability P(Y(t)>3), when E[Y2(t)] = 10.