Lehmer Transform and its Theoretical Properties

TL;DR

The paper introduces the Lehmer Transform, a new mathematical tool inspired by the Lehmer mean, which decomposes functions into moments and has potential applications in analyzing non-stationary signals like EEG.

Contribution

It presents the Lehmer Transform and explores its theoretical properties, offering a novel approach for signal analysis.

Findings

The Lehmer Transform decomposes functions into statistical moments.

Theoretical properties of the Lehmer Transform are established.

Potential application in EEG signal analysis.

Abstract

We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical moments. Theoretical properties of the proposed transform are presented. This transform could be very useful to provide an alternative method in analyzing non-stationary signals such as brain wave EEG.