This paper gives a systematic approach to generate a Markov chain by a discrete-valued auto-regressive equation, which is a a nonlinear auto-regressive equation having a discrete-valued solution. The power spectrum, the correlation function and the transition probability are explicitly obtained in terms of the discrete-valued auto-regressive equation. Some computer results are illustrated in figures.

As a new method to generate a homogeneous, random, binary image with a rational power spectrum, this paper proposes a discrete-valued auto-regressive equation, of which random coefficients and white noise excitation are all discrete-valued. The average and spectrum of the binary image are explicitly obtained in terms of the random coefficients. Some computer results are illustrated in figures.

This paper proposes a second order auto-regressive equation with discrete-valued random coefficients. The auto-regressive equation transforms an independent stochastic sequence into a binary sequence, which is a special case of a stationary Markov chain. The power spectrum, correlation function and the transition probability are explicitly obtained in terms of the random coefficients. Some computer results are illustrated in figures.