Uniqueness of the impulse function of a discrete-time Markov process

The object of the letter is to find a unique function of n which represents the inverse z transform of unity (1) in the analysis of a finite-state Markov process. The function of n is found to be the sum of two ordinary step functions. The necessary and sufficient conditions for the existence of a one in the z domain in the analysis of a Markov process are determined. Using the necessary and sufficient conditions, the various configurations of the Markov process in which this situation exists are investigated.