Statistical Analysis of Synchrosqueezed Transforms

2014/10/22 by Haizhao Yang, Yang, Haizhao · 1 citation
Computer Science · Engineering · #FOS: Mathematics #Image and Signal Denoising Methods #Machine Fault Diagnosis Techniques #Numerical Analysis (math.NA) #Statistics Theory (math.ST) #Structural Health Monitoring Techniques

paper · pdf · doi:10.48550/arxiv.1410.5939

openalex publication_date 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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