Diffusion Approximations for the Analysis of Digital Phase Locked Loops,

Abstract

Recent results for getting diffusion limits of a sequence of suitably scaled stochastic processes are applied to the synchronization problem for a digital phase locked loop (DPLL). The discrete time parameter error processes is suitably amplitude scaled and interpolated into a continuous time parameter process. For small filter gains and symbol intervals, a diffusion process approximation is rigorously obtained. This approximation is a Gauss-Markov process and it yields approximate error variances, passage time distributions, correlation properties, (among other properties) for the DPLL. The tracking problem when the clock drifts is also treated. The technique is applicable to a wide variety of related problems, to get continuous time Markov systems which are easier to analyze the original (continuous or discrete time) systems which they approximate. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1980
Accession Number
ADA088703

Entities

People

  • Hai Huang
  • Harold J. Kushner

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Clocks
  • Convergence
  • Difference Equations
  • Differential Equations
  • Diffusion
  • Equations
  • Interpolation
  • Markov Processes
  • Mathematics
  • Probability
  • Random Variables
  • Sequences
  • Stochastic Processes
  • Time Intervals
  • Weak Convergence

Readers

  • Approximation Theory.
  • Mathematical Modeling and Probability Theory.
  • Radio communications and signal processing.