The signal y(t) = e-2t u(t) is the output of a causal all-pass system for which the
Chapter 9, Problem 9.47(choose chapter or problem)
The signal y(t) = e-2t u(t) is the output of a causal all-pass system for which the system function is s- 1 H(s) = s + 1' (a) Find and sketch at least two possible inputs x(t) that could produce y(t). (b) What is the input x(t) if it is known that roo lx(tll dt < oo? (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)].
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