A Unified Theory of Time-Frequency Reassignment

TL;DR

This paper provides a comprehensive theoretical framework for the method of time-frequency reassignment, unifying various implementations and discussing its applications in improving spectral resolution in signal analysis.

Contribution

It offers a unified mathematical description of time-frequency reassignment, clarifying its foundations and development history, and discusses its application to spectrogram analysis.

Findings

Unified mathematical framework for reassignment methods

Enhanced spectral resolution in time-frequency analysis

Discussion of practical applications in signal processing

Abstract

Time-frequency representations such as the spectrogram are commonly used to analyze signals having a time-varying distribution of spectral energy, but the spectrogram is constrained by an unfortunate tradeoff between resolution in time and frequency. A method of achieving high-resolution spectral representations has been independently introduced by several parties. The technique has been variously named reassignment and remapping, but while the implementations have differed in details, they are all based on the same theoretical and mathematical foundation. In this work, we present a brief history of work on the method we will call the method of time-frequency reassignment, and present a unified mathematical description of the technique and its derivation. We will focus on the development of time-frequency reassignment in the context of the spectrogram, and conclude with a discussion of some current applications of the reassigned spectrogram.