# Second-order Time-Reassigned Synchrosqueezing Transform: Application to Draupner Wave Analysis

## TL;DR

This paper introduces a second-order time-reassigned synchrosqueezing transform that improves time-frequency analysis of impulsive and modulated signals, demonstrated on synthetic data and pioneering analysis of Draupner wave records.

## Contribution

It presents a novel second-order enhancement of the synchrosqueezing transform for better joint time-frequency representation of complex signals.

## Key findings

- Enhanced time-frequency resolution for impulsive signals
- Reversible and sharpened signal representations achieved
- First detailed analysis of Draupner wave in time-frequency domain

## Abstract

This paper addresses the problem of efficiently jointly representing a non-stationary multicomponent signal in time and frequency. We introduce a novel enhancement of the time-reassigned synchrosqueezing method designed to compute sharpened and reversible representations of impulsive or strongly modulated signals. After establishing theoretical relations of the new proposed method with our previous results, we illustrate in numerical experiments the improvement brought by our proposal when applied on both synthetic and real-world signals. Our experiments deal with an analysis of the Draupner wave record for which we provide pioneered time-frequency analysis results.