Statistical Analysis of Synchrosqueezed Transforms

TL;DR

This paper investigates the statistical properties of synchrosqueezed transforms in noisy environments, proposing new numerical methods to enhance their noise robustness and providing a MATLAB package for practical use.

Contribution

It offers a theoretical analysis of synchrosqueezed transforms' statistical behavior and introduces improved numerical implementations to reduce noise fluctuations.

Findings

Theoretical insights into the statistical properties of synchrosqueezed transforms.

Development of numerical methods to suppress noise in transforms.

Provision of a MATLAB package with noisy examples for validation.

Abstract

Synchrosqueezed transforms are non-linear processes for a sharpened time-frequency representation of wave-like components. They are efficient tools for identifying and analyzing wave-like components from their superposition. This paper is concerned with the statistical properties of compactly supported synchrosqueezed transforms for wave-like components embedded in a generalized Gaussian random process in multidimensional spaces. Guided by the theoretical analysis of these properties, new numerical implementations are proposed to reduce the noise fluctuations of these transforms on noisy data. A MATLAB package SynLab together with several heavily noisy examples is provided to support these theoretical claims.