In the concept of correlation functions , it is often important in practice to compute the correlation function

, where h (t) is a fixed given signal, but where x (t) may be any of a wide variety of signals. Let S be the system which takes x (t) as the input and gives as the output .

(a) Is S linear ? Is S time invariant ? Is S causal ? Explain your answers .

(b) Do any of your answer to above part change if we take as the output instead of ?