A linear time-invariant system has an input sequence x(n) and an output sequence y(n). The user has access only to the system output y(n). In addition, the following information is available:
The input signal is periodic with a given fundamental period N and has a flat spectral envelop; that is,
where for all k.
The system H(z) is all pole, that is,
but the order p and the coefficients are unknown. Is it possible to determine the order p and the numerical values of the coefficients by taking measurements on the output y(n)? If yes, explain how. Is this possible for every value of p?
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