Analysis of time-varying signals using continuous wavelet and synchrosqueezed transforms

Abstract

The continuous wavelet transform (CWT) has played a key role in the analysis of time-frequency information in many different fields of science and engineering. It builds on the classical short-time Fourier transform but allows for variable time-frequency resolution. Yet, interpretation of the resulting spectral decomposition is often hindered by smearing and leakage of individual frequency components. Computation of instantaneous frequencies, combined by frequency reassignment, may then be applied by highly localized techniques, such as the synchrosqueezing transform and ConceFT, in order to reduce these effects. In this paper, we present the synchrosqueezing transform together with the CWT and illustrate their relative performances using four signals from different fields, namely the LIGO signal showing gravitational waves, a 'FanQuake' signal displaying observed vibrations during an American football game, a seismic recording of the 8.2 Chiapas earthquake, Mexico, of 8 September 2017, followed by the Irma hurricane, and a volcano-seismic signal recorded at the Popocatépetl volcano showing a tremor followed by harmonic resonances. These examples illustrate how high-localization techniques improve analysis of the time-frequency information of time-varying signals.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Параметры Фазовой Синхронизации В Электроэнцефалографических Паттернах Как Маркеры Когнитивных Нарушений

“…Интерпретация результирующего спектрального разложения часто затрудняется размытием некоторых частотных составляющих анализируемого сигнала [22]. Уменьшить эти эффекты можно с использованием метода синхросжатого вейвлет-преобразования [23].…”

Windowed multiscale synchrony: modeling time-varying and scale-localized interpersonal coordination dynamics

“…This generalization would broaden WMS’ applicability to understanding coordination in groups larger than dyads and in cases such as neurophysiology where there are many data streams. Lastly, wavelet-based methods, which are known to suffer from frequency smearing and edging effects, may be improved by incorporating synchrosqueezed transformations ( Tary et al , 2018 ), so this is also likely a worthwhile area of investigation for WMS as well.…”

Research and Application of Acoustic Emission Signal Processing Technology

“…Fourier transform reflects the integral characteristics of signal or function, but it can not display the characteristics of signal in local time range. Wavelet analysis has a very good frequency resolution at the low frequency end of the signal, while the frequency resolution at the high frequency end is very weak, which just makes up for Fourier's shortcomings [34]. Wavelet transform decomposes signals at different scales to extract their characteristics, or to analyze the results of time-frequency decomposition for signal processing [35].…”