Suppose that we are given a causal LTI system characterized by its impulse response, h(t). If this system is excited by zero-mean, unit variance white noise, then (a) Determine the output variance,...

Suppose that we are given a causal LTI system characterized by its impulse response, h(t). If this system is excited by zero-mean, unit variance white noise, then

(a) Determine the output variance, Ryy (0).

(b) Determine the covariance, Ryy (k) for k > 0.

(c) Suppose that the system transfer function is given by

Find a method to recursively calculate h(t) and therefore Ryy (0).