Stable probability laws modeling random propagation times of waves crossing different media

TL;DR

This paper models wave propagation times across various media using stable probability laws, explaining spectral changes in acoustic, ultrasonic, and electromagnetic waves with a focus on causality constraints.

Contribution

It introduces stable probability law models for wave propagation times, linking them to physical media and causality in linear systems.

Findings

Stable laws explain spectral features in wave propagation.

Models apply to acoustics, ultrasonics, and electromagnetics.

Causality constrains the form of the probability laws.

Abstract

In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in electrical cables which preceed or follow antennas. In many cases, a random propagation time is sufficient to explain changes induced by the medium. In this paper we study models based on stable probability laws which explain power spectra due to propagation of different kinds of waves in different media, for instance, acoustics in quiet or turbulent atmosphere, ultrasonics in liquids or tissues, or electromagnetic waves in free space or in cables. Physical examples show that a sub-class of probability laws appears in accordance with the causality property of linear filters.