The signal is the output of a casual all-pass system for which the system funct...

The signal

is the output of a casual all-pass system for which the system function is

(a) Find and sketch at least two possible input(t) that could produce y(t).

(b) What is the input x(t) if it is known that

(c) What is the input x(t) if it is known that a stable (but not necessarily causal system exists that will have x(t) as an output if y(t) is the input? Find the impulse response h(t) of this filter, and show by direct convolution that it has the property claimed [i.e., that y(t) ∗ h(t) = x(t)].