Some Comments on sampling of ergodic process, an Ergodic theorem and turbulent pressure fluctuations

TL;DR

This paper introduces a novel proof of an ergodic theorem for wide-sense stationary processes and a new sampling theorem for finite signals in the frequency domain, avoiding Nyquist limitations.

Contribution

It provides a new ergodic theorem proof and a canonical sampling theorem that applies to finite signals without Nyquist restrictions, useful for modeling pressure fluctuations.

Findings

New proof of ergodic theorem for wide-sense stationary processes

Canonical sampling theorem free from Nyquist interval restrictions

Application to modeling turbulent pressure fluctuations

Abstract

We present a new proof of an Ergodic theorem for Wide-Sense Stationary Random Processes added with a new canonical sampling theorem of mine for finite time duration signals in the frequency domain (periodograms) which is free from the Nyquist interval restriction.We point out the usefulness of such theorem in the context of a model of random vibrations transmission (pressure-explosive fluctuations).Replacement due to inadvertent and wrong acknowledgments