Analysis of adaptive synchrosqueezing transform with a time-varying parameter

Lü, Jian; Jiang, Qingtang; Li, Lin

doi:10.1007/s10444-020-09814-x

Cited by 18 publications

(6 citation statements)

References 44 publications

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“…They obtained the well-separated condition for multicomponent signals using the linear frequency modulation signals to approximate a non-stationary signal at any local time. The theoretical analysis of second-order adaptive FSST and WSST was studied in [3] and [19], respectively. In this paper we consider an FSST2 with a phase transformation which has a simpler expression than that used in the literature.…”

Section: Introductionmentioning

confidence: 99%

A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

Lü¹

2021

NMTMA

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To model a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes is important to extract information, such as the underlying dynamics, hidden in the signal. Recently, the synchrosqueezed wavelet transform (SST) and its variants have been developed to estimate instantaneous frequencies and separate the components of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST for short) reassigns the frequency variable to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. However FSST works well only with multicomponent signals having slowly changing frequencies. To deal with multicomponent signals having fast-changing frequencies, the secondorder FSST (FSST2 for short) was proposed. The key point for FSST2 is to construct a phase transformation of a signal which is the instantaneous frequency when the signal is a linear chirp. In this paper we consider a phase transformation for FSST2 which has a simple expression than that used in the literature. In the study the theoretical analysis of FSST2 with this phase transformation, we observe that the proof for the error bounds for the instantaneous frequency estimation and component recovery is simpler than that with the conventional phase transformation. We also provide some experimental results which show that this FSST2 performs well in non-stationary multicomponent signal separation.

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Section: Introductionmentioning

confidence: 99%

A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

Lü¹

2021

NMTMA

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“…An adaptive SST with a time-varying parameter was recently introduced in [34,35], which obtains the well-separated condition for multi-component signals using the linear frequency modulation to approximate a non-stationary signal at every time instant. The theoretical analysis of adaptive SST was studied in [36,37]. Finally, combining the SST with the ideal TF representation theory, the synchroextracting transform (SET) [38] was proposed to improve the TF concentration by extracting the ridges of the STFT.…”

Section: Introductionmentioning

confidence: 99%

IF equation: a feature extractor for high-concentration time-frequency representation

Zhu¹,

Yang²,

Zhang

2021

Preprint

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High-concentration time-frequency (TF) representation provides a valuable tool for characterizing multicomponent non-stationary signals. In our previous work, we proposed using an instantaneous frequency (IF) equation to sharpen the TF distribution and its effectiveness has been verified in experiments. In this paper, we systematically discuss why the IF equation-based TF analysis methods work and how to use the IF equation to improve the TF sharpness. By theory analysis, many popular TF post-processing methods, such as the synchroextracting transform, the multi-synchrosqueezing transform, and the time extracting transform, fall into the IF equation-based category. A comparison of the IF equation-based method with the popular synchrosqueezing transform is made. Numerical examples of the theoretical derivations are presented to illustrate the performance of the proposed IF equation-based TF analysis method.

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“…SST provides an alternative to the EMD method and its variants, and it overcomes some limitations of the EMD scheme [1]. Other types of SST, such as SST with vanishing moment wavelets with stacked knots [8], a hybrid EMT-SST computational scheme [11], matching demodulation transform-based SST [21,43,20,44], synchrosqueezed curvelet transform [50], synchrosqueezed wave packet transforms [49], the SST based on S-transform [19], the 2nd-order SST [33,30,2,34], the adaptive SST [39,3,22,23,5,29], have been proposed and studied.…”

Section: Introductionmentioning

confidence: 99%

Signal Separation Based on Adaptive Continuous Wavelet Transform and Analysis

Chui¹,

Jiang²,

Li³

et al. 2020

Preprint

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In nature and engineering world, the measured signals are usually affected by multiple complicated factors and they appear as multicomponent non-stationary modes. In many situations we need to separate these signals to a finite number of mono-components to represent the intrinsic modes and underlying dynamics implicated in the source signals. Recently the synchrosqueezing transform (SST) was developed as an empirical mode decomposition (EMD)-like tool to enhance the time-frequency resolution and energy concentration of a multicomponent non-stationary signal and provides more accurate component recovery. To recover individual components, the SST method consists of two steps. First the instantaneous frequency (IF) of a component is estimated from the SST plane. Secondly, after IF is recovered, the associated component is computed by a definite integral along the estimated IF curve on the SST plane. The reconstruction accuracy for a component depends heavily on the accuracy of the IFs estimation carried out in the first step.More recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced for multicomponent signal separation. While both SST and SSO are mathematically rigorous on IF estimation, SSO avoids the second step of the two-step SST method in component recovery (mode retrieval).The SSO method is based the short-time Fourier transform. In this paper we propose a direct method of signal separation based on the adaptive continuous wavelet transform (CWT). We introduce two models of the adaptive CWT-based approach for signal separation: the sinusoidal signal-based model and the linear chirp-based model, which are derived respectively from

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Analysis of adaptive synchrosqueezing transform with a time-varying parameter

Cited by 18 publications

References 44 publications

A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

A Second-Order Synchrosqueezing Transform with a Simple Form of Phase Transformation

IF equation: a feature extractor for high-concentration time-frequency representation

Signal Separation Based on Adaptive Continuous Wavelet Transform and Analysis

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