Analysis of a Direct Separation Method Based on Adaptive Chirplet Transform for Signals with Crossover Instantaneous Frequencies

TL;DR

This paper conducts an in-depth error analysis of a novel adaptive chirplet transform-based method for separating and recovering components of multi-component signals, especially those with crossing instantaneous frequencies.

Contribution

It provides a detailed error analysis of the CT3S method, extending signal separation capabilities beyond traditional frequency separation constraints.

Findings

Error bounds for instantaneous frequency estimation

Improved component recovery accuracy

Effective separation of crossing frequency components

Abstract

In many applications, it is necessary to retrieve the sub-signal building blocks of a multi-component signal, which is usually non-stationary in real-world and real-life applications. Empirical mode decomposition (EMD), synchrosqueezing transform (SST), signal separation operation (SSO), and iterative filtering decomposition (IFD) have been proposed and developed for this purpose. However, these computational methods are restricted by the specification of well-separation of the sub-signal frequency curves for multi-component signals. On the other hand, the chirplet transform-based signal separation scheme (CT3S) that extends SSO from the two-dimensional "time-frequency" plane to the three-dimensional "time-frequency-chirp rate" space was recently proposed in our recent work to remove the frequency-separation specification, and thereby allowing "frequency crossing". The main objective of this present paper is to carry out an in-depth error analysis study of instantaneous frequency estimation and component recovery for the CT3S method.