Generating Binary Processes with all-Pole Spectra

This paper presents an algorithm to generate autoregressive random binary processes with predefined mean and predefined all-pole power spectrum, subject to specific constraints on the parameters of the all-pole spectrum. The process is generated recursively using a linear combination of the previously generated values to bias the generation of the next value. It is shown that an all-zero filter whitens the process, and, therefore, the process has an all-pole spectrum. The process is also described using an ergodic Markov chain, which is used to determine the appropriate initialization and to prove convergence if the algorithm is not initialized properly. The all-pole parameter range for which the algorithm is guaranteed to work is also derived. It is shown to be a linear constraint on the all-pole parameters and their magnitude, subject to the desired mean for the process. The example and simulations presented elucidate and confirm the theoretic developments.