Adaptive Energy Saving Approximation for Random Stationary Processes

TL;DR

This paper introduces an adaptive approximation method for stationary processes that balances approximation accuracy with energy efficiency and smoothness, using spectral analysis and classical prediction theory.

Contribution

It presents a novel adaptive approximation framework for stationary processes that optimally combines approximation quality with energy and smoothness considerations.

Findings

Effective spectral-based approximation method developed.

Balances approximation accuracy with energy and smoothness.

Applicable to both discrete and continuous-time processes.

Abstract

We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional smoothness or small expense of energy. The problem is solved in terms of the spectral characteristics of the approximated process by using classical analytic methods from prediction theory.