Symplectic Transformations on Wigner Distributions and Time Frequency Signal Design

TL;DR

This paper explores uncertainty relations in time-frequency distributions, using quantum mechanics concepts to analyze how signal transformations affect variances and uncertainty bounds in signal processing.

Contribution

It introduces a novel analysis of uncertainty relations on marginalizable time-frequency distributions and studies transformations that preserve these relations.

Findings

Uncertainty relations are established for marginalizable time-frequency distributions.

Certain signal operations are identified that leave uncertainty bounds unchanged.

Quantum mechanics principles are applied to analyze variance changes in time and frequency.

Abstract

This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on Wigner distributions and marginalizable time frequency distributions to investigate the change in variance of time and frequency variables from a signal processing perspective. Moreover, operations on signals which leave uncertainty relations unchanged are studied.