Extracting Phases from Aperiodic Signals

TL;DR

This paper discusses the fundamental challenge of defining phase in aperiodic signals and proposes a decomposition method into components with positive phase velocities as a solution.

Contribution

It highlights the fundamental issues in phase definition for aperiodic signals and revisits an existing decomposition approach as a potential remedy.

Findings

The phase definition problem is more serious than previously thought.

Decomposition into positive phase velocity components offers a promising solution.

The paper emphasizes the importance of proper phase extraction in signal analysis.

Abstract

We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive phase velocities is proposed as an old solution to this new problem.