Markov Models for Coherent Signals: Extrapolation in the Frequency Domain

Introduction

In this paper we describe a Markov model for a class of stochastic processes whose properties relate to a wide variety of situations in which time-frequency analysis is relevant. These include the production of sound and, in particular, music, frequency modulated digital communication systems, stimulated emission in atomic physics and other aspects of coherent light.More specifically, it provides a new point of view on some ideas explored over the years by Yutaka Yamamoto [1, 2, 3] and others [4] relating to the regeneration of sound from compressed versions obtained by band limiting and sampling. We frame this particular question as one of extrapolation in the frequency domain and argue that analytically tractable signal models can play a significant role in facilitating the reconstruction process. We also touch briefly on the data needed for parameter selection and model validation.

This work was supported in part by the US Army Research Office under grant DAAG 55 97 1 0114.