For the high pass RC network shown, let X (t) A sin ( Iuml ct Icirc cedil ) N (t), where is white, WSS, Gaussian noise and Icirc cedil is a random variable uniformly distributed over 0, 2 Iuml Assuming zero initial conditions (a) Find the output mean and variance (b) Find and plot the autocorrelati...

For this filter the transfer function and the impulse response are The inp ...

For the high- pass RC network shown, let X (t) = A sin (Ï ct + Î¸)

Question:

For the high- pass RC network shown, let X (t) = A sin (Ï‰ ct + Î¸) + N (t), where is white, WSS, Gaussian noise and Î¸ is a random variable uniformly distributed over [0, 2Ï€]. Assuming zero initial conditions:
(a) Find the output mean and variance.
(b) Find and plot the autocorrelation function of the output.
(c) Find and plot the output PSD.
(d) Find the output SNR.