Jacob's ladders, $\mathcal{Z}_{\zeta,Q^2}$-transformation of real elementary functions and telegraphic signals generated by the power functions

TL;DR

This paper demonstrates that applying the $\\mathcal{Z}_{\zeta,Q^2}$-transformation to unbounded signals derived from increasing power functions results in a telegraphic, rectangular signal, revealing a novel signal transformation property.

Contribution

It introduces a new transformation that converts unbounded power-based signals into rectangular telegraphic signals, expanding understanding of signal transformations.

Findings

Transformation converts unbounded power signals into rectangular signals

Reveals a new link between power functions and telegraphic signals

Potential applications in signal processing and analysis

Abstract

In this paper we show that the $\mathcal{Z}_{\zeta,Q^2}$-transformation of every unbounded signal based on increasing power function is a telegraphic signal, i.e. the unit rectangular signal.