On the statistics of the error in predictive coding for stationary Ornstein-Uhlenbeck processes

Author

Koski, Timo ; Cambanis, Stamatis

Author_Institution

Dept. of Syst. Eng. & Math., Lulea Univ. of Technol., Sweden

Volume

38

Issue

3

fYear

1992

fDate

5/1/1992 12:00:00 AM

Firstpage

1029

Lastpage

1040

Abstract

Explicit expression are derived for the conditional expectation and variance of the encoder in a predictive DPCM coder with an N-level quantizer, when a stationary Ornstein-Uhlenbeck process is a source. A representation of the encoder in terms of a stochastic integral is presented. These expressions yield a nonlinear stochastic difference equation for the decoding error process and a stochastic differential equation (SDE) as a weak limit for the error process. The statistical properties of the error obtained as a solution of the limiting SDE are interpreted in terms of the slope overload error

Keywords

decoding; difference equations; differential equations; encoding; error statistics; filtering and prediction theory; pulse-code modulation; stochastic processes; DPCM coder; N-level quantizer; conditional expectation; decoding error process; encoder; error statistics; nonlinear stochastic difference equation; predictive coding; slope overload error; stationary Ornstein-Uhlenbeck processes; stochastic differential equation; stochastic integral; variance; Decoding; Delta modulation; Difference equations; Differential equations; Error analysis; Nonlinear equations; Predictive coding; Pulse modulation; Stability; Stochastic processes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.135643

Filename

135643