Spectral Analysis of Functions of Markov Chains with Applications

TLDR: Under the assumption that the Markov chain is ergodic, not necessarily acyclic, closed form formulas are derived for both the discrete part and the continuous part of the spectral density of digital processes obtained through memoryless functions of stationary Markov chains.

Abstract: This paper deals with the spectral analysis of digital processes obtained through memoryless functions of stationary Markov chains. Under the assumption that the Markov chain is ergodic, not necessarily acyclic, closed form formulas are derived for both the discrete part (spectral lines) and the continuous part of the spectral density. The results are applied at the output of a finite state sequential machine driven by a stationary Markov chain, which represents a general model of several situations of engineering interest. Finally, the theory is used to evaluate the spectrum of encoded and modulated digital signals.