A Characterization of Metaplectic Time-Frequency Representations

TL;DR

This paper characterizes all time-frequency representations that are covariant under time-frequency shifts, showing they are essentially multiples of metaplectic representations, thus providing a comprehensive understanding of their structure.

Contribution

It provides a complete characterization of covariant time-frequency representations, identifying them as multiples of metaplectic representations, which advances theoretical understanding in the field.

Findings

All covariant time-frequency representations are multiples of metaplectic representations.

The characterization applies to weak*-continuous bilinear mappings.

This unifies various time-frequency representations under a common framework.

Abstract

We characterize all time-frequency representations that satisfy a general covariance property: any weak*-continuous bilinear mapping that intertwines time-frequency shifts on the configuration space with time-frequency shifts on phase space is a multiple of a metaplectic time-frequency representation.