A chirplet transform-based mode retrieval method for multicomponent signals with crossover instantaneous frequencies

Lin Li, Ningning Han, Qingtang Jiang, Charles K. Chui

Research output: Contribution to journalArticlepeer-review

Abstract

In nature and engineering world, the acquired signals are usually affected by multiple complicated factors and appear as multicomponent nonstationary modes. In such and many other situations, it is necessary to separate these signals into a finite number of monocomponents to represent the intrinsic modes and underlying dynamics implicated in the source signals. In this paper, we consider the mode retrieval of a  multicomponent signal  which has crossing  instantaneous frequencies  (IFs), meaning that some of the components of the signal overlap in the time-frequency domain. We use the chirplet transform (CT) to represent a multicomponent signal in the three-dimensional space of time, frequency and chirp rate and introduce a CT-based signal separation scheme (CT3S) to retrieve modes. In addition, we analyze the error bounds for IF estimation and component recovery with this scheme. We also propose a matched-filter along certain specific time-frequency lines with respect to the chirp rate to make  nonstationary signals  be further separated and more concentrated in the three-dimensional space of CT. Furthermore, based on the approximation of source signals with  linear chirps  at any local time, we propose an innovative signal reconstruction algorithm, called the group filter-matched CT3S (GFCT3S), which also takes a group of components into consideration simultaneously. GFCT3S is suitable for signals with crossing IFs. It also decreases component recovery errors when the IFs curves of different components are not crossover, but fast-varying and close to each other. Numerical experiments on synthetic and real signals show our method is more accurate and consistent in signal separation than the empirical mode decomposition, synchrosqueezing transform, and other approaches.

Original languageAmerican English
JournalDigital Signal Processing
Volume120
DOIs
StatePublished - Jan 2022

Keywords

  • Chirplet transform
  • Filter-matched chirplet transform
  • Mode retrieval
  • Multicomponent signals with crossing instantaneous frequencies
  • Signal separation

Disciplines

  • Physical Sciences and Mathematics

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