Consider a discrete-time LTI system with a real-valued impulse response h[n].We want to find h[n], or equivalently, the system function H(z) from the autocorrelation chh [] of the impulse response. The definition of the autocorrelation is
(a) If the system h[n] is causal and stable, can you uniquely recover h[n] from chh[ ]? Justify your answer.
(b) Assume that h[n] is causal and stable and that, in addition, you know that the system function has the form
for some finite ak . Can you uniquely recover h[n] from chh []? Clearly justify your answer.
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