In Problem 1.37, we introduced the concept of correlation functions. It is often importa...

In Problem 1.37, we introduced 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. In this case, what is done is to design a system S with input x(t) and output .

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

(b) Do any of your answers to part (a) change if we take as the output rather than ?

Reference: Problem 1.37

In Problem 1.37, we introduced the concept of correlation functions. It is often important in practice to compute the correlation function .

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

(b) Do any of your answers to part (a) change if we take as the output ?

Reference: Problem 1.37