A linear time-invariant system has an input sequence x(n) and an output sequence y(n). T...

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?