Average sampling restoration of harmonizable processes

TL;DR

This paper introduces a method for approximating harmonizable Piranashvili-type stochastic processes using finite average sampling sums, providing explicit error bounds and discussing special cases.

Contribution

It presents a novel approach for process approximation with explicit error bounds, enhancing sampling theory for harmonizable processes.

Findings

Explicit truncation error bounds are derived.

The method applies to various special cases.

The approach improves process approximation accuracy.

Abstract

The harmonizable Piranashvili-type stochastic processes are approximated by finite time shifted average sampling sums. Explicit truncation error upper bounds are established. Various corollaries and special cases are discussed.