Consider a discrete-time LTI system with a real-valued impulse response h[n].We want to...

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 c_hh [] 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 c_hh[ ]? 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 a_k . Can you uniquely recover h[n] from c_hh []? Clearly justify your answer.