重新分配和同步压缩笔记

This article provides a general overview of time-frequency (T-F) reassignment and synchrosqueezing techniques applied to multicomponent signals, covering the theoretical background and applications, explaining how synchrosqueezing can be viewed as a special case of reassignment enabling mode reconstruction.

Introduction

Generalizing Fourier analysis can be understood in two complementary (互补的) ways:

• The frist attempts to make the Fourier transform time dependent, linear, with a complex-valued frequency description that involves magnitude (幅值) and phase contributions
• The second focuses on the associated spectral density (密度), quadratic (二次), leads to real-valued transforms in most cases

Wiigner-Ville distribution (WVD)

Synchrosqueezing’s purpose was very similar to reassignment (indeed it is a special case), with the additioinal advantage of allowing for reconstruction. The purpose of this article is to offer a brief guided tour emphasizing key features of both techniques, clarifying their relationships, and illustrating them with some example applications.