.4. (21 Pts) System Response to White Noise Zero-mean white noise X(t) with power spectral density Sx () = So = 8 enters a LTI system with transfer function 8 8 H (s) = 8² +48 +3 (8+1)(8+3) 1 (a) (7 Pts) Find the PSD Sy (w) of the output Y (t). Hint: Recall that H (w) = H (8)|=j (b) (9 Pts) Find the autocorrelation Ry (7) and average power Py of the output (c) (5 Pts) Does Y(t) have a DC component? Does Y(t) have a AC component? Explain why?