arXiv subjects

Qingtang Jiang

Publications and source records attributed to Qingtang Jiang.

17 recordsLinked to original sources

arXiv2026

High-order synchrosqueezed wavelet-chirplet transform for instantaneous frequency and chirprate estimation

The separation of multicomponent signals with crossing instantaneous frequency (IF) curves remains a fundamental challenge in time-frequency analysis. Although the synchrosqueezed wavelet-chirplet transform (SWCT) enhances time-frequency readability by introducing a chirprate variable, its effectiveness is constrained by the underlying assumption of local linear chirp. Consequently, this method does not perform well when analyzing signals characterized by strong frequency modulation. This paper extends the SWCT framework by relaxing the linear chirp assumption. We model signal components as having polynomial phase behavior over short intervals and derive compact expressions for high-order IF and chirprate reassignment operators. The proposed high-order synchrosqueezed wavelet-chirplet transform (HSWCT) enables accurate estimation of both IF and chirprate, and supports robust mode retrieval even with intersecting IF curves. Another key contribution is a rigorous mathematical analysis of the approximation errors of arbitrary-order reassignment operators for IF and chirprate estimation. When the chirprate vanishes, HSWCT simplifies to the traditional high-order synchrosqueezed wavelet transform. To our best knowledge, no theoretical analysis exists in the literature on the approximation of arbitrary-order SST IF reassignment operators to the IF. As a by-product of this work, our established theorem provides such an analysis, thereby filling a gap in the theoretical framework of high-order SSTs.

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arXiv2025

Synchrosqueezed windowed linear canonical transform: A method for mode retrieval from multicomponent signals with crossing instantaneous frequencies

In nature, signals often appear in the form of the superposition of multiple non-stationary signals. The overlap of signal components in the time-frequency domain poses a significant challenge for signal analysis. One approach to addressing this problem is to introduce an additional chirprate parameter and use the chirplet transform (CT) to elevate the two-dimensional time-frequency representation to a three-dimensional time-frequency-chirprate representation. From a certain point of view, the CT of a signal can be regarded as a windowed special linear canonical transform of that signal, undergoing a shift and a modulation. In this paper, we develop this idea to propose a novel windowed linear canonical transform (WLCT), which provides a new time-frequency-chirprate representation. We discuss four types of WLCTs. In addition, we use a special X-ray transform to further sharpen the time-frequency-chirprate representation. Furthermore, we derive the corresponding three-dimensional synchrosqueezed transform, demonstrating that the WLCTs have great potential for three-dimensional signal separation.

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arXiv2025

Time-reassigned synchrosqueezing frequency-domain chirplet transform for multicomponent signals with intersecting group delay curves

To analyze signals with rapid frequency variations or transient components, the time-reassigned synchrosqueezing transform (TSST) and its variants have been recently proposed. Unlike the traditional synchrosqueezing transform, TSST squeezes the time-frequency (TF) coefficients along the group delay (GD) trajectories rather than the instantaneous frequency trajectories. Although TSST methods perform well in analyzing transient signals, they are fundamentally limited in processing multicomponent signals with intersecting GD curves. This limitation compromises the accuracy of both feature extraction and signal component recovery, thereby significantly reducing the interpretability of time-frequency representations (TFRs). This is particularly problematic in broadband signal processing systems, where the linearity of the phase response is critical and precise measurement of group delay dispersion (GDD) is essential. Motivated by the superior capability of frequency-domain signal modeling in characterizing rapidly frequency-varying signals, this paper proposes a novel three-dimensional time-frequency-group delay dispersion (TF-GDD) representation based on the frequency-domain chirplet transform. A subsequent time-reassigned synchrosqueezing frequency-domain chirplet transform (TSFCT) is introduced to achieve a sharper TF-GDD distribution and more accurate GD estimation. For mode retrieval, a novel frequency-domain group signal separation operation (FGSSO) is proposed.The theoretical contributions include a derivation of the approximation error for the GD and GDD reference functions and an establishment of the error bounds for FGSSO-based mode retrieval. Experimental results demonstrate that the proposed TSFCT and FGSSO effectively estimate GDs and retrieve modes--even for modes with intersecting GD trajectories.

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arXiv2025

Synchrosqueezed X-Ray Wavelet-Chirplet Transform for Accurate Chirp Rate Estimation and Retrieval of Modes from Multicomponent Signals with Crossover Instantaneous Frequencies

Recent advances in the chirplet transform and wavelet-chirplet transform (WCT) have enabled the estimation of instantaneous frequencies (IFs) and chirprates, as well as mode retrieval from multicomponent signals with crossover IF curves. However, chirprate estimation via these approaches remains less accurate than IF estimation, primarily due to the slow decay of the chirplet transform or WCT along the chirprate direction. To address this, the synchrosqueezed chirplet transform (SCT) and multiple SCT methods were proposed, achieving moderate improvements in IF and chirprate estimation accuracy. Nevertheless, a novel approach is still needed to enhance the transform's decay along the chirprate direction. This paper introduces an X-ray transform-based wavelet-chirprate transform, termed the X-ray wavelet-chirplet transform (XWCT), which exhibits superior decay along the chirprate direction compared to the WCT. Furthermore, third-order synchrosqueezed variants of the WCT and XWCT are developed to yield sharp time-frequency-chirprate representations of signals. Experimental results demonstrate that the XWCT achieves significantly faster decay along the chirprate axis, while the third-order synchrosqueezed XWCT enables accurate IF and chirprate estimation, as well as mode retrieval, without requiring multiple synchrosqueezing operations.

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arXiv2024

Synchro-Transient-Extracting Transform for the Analysis of Signals with Both Harmonic and Impulsive Components

Time-frequency analysis (TFA) techniques play an important role in the field of machine fault diagnosis attributing to their superiority in dealing with nonstationary signals. Synchroextracting transform (SET) and transient-extracting transform (TET) are two newly emerging techniques that can produce energy concentrated representation for nonstationary signals. However, SET and TET are only suitable for processing harmonic signals and impulsive signals, respectively. This poses a challenge for each of these two techniques when a signal contains both harmonic and impulsive components. In this paper, we propose a new TFA technique to solve this problem. The technique first divides time-frequency (TF) coefficients into two types according to the chirp rate of the signal, and then TF ridges are respectively extracted to prevent the limitation for the independent use of SET and TET. This allows the technique to generate an energy-concentrated TF representation for both harmonics and impulses in the signal. Furthermore, we theoretically demonstrate that the proposed technique retains the signal reconstruction capability. The effectiveness of the proposed technique is verified using numerical and real-world signals.

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arXiv2022

Direct Signal Separation Via Extraction of Local Frequencies with Adaptive Time-Varying Parameters

Real-world phenomena that can be formulated as signals are often affected by a number of factors and appear as multi-component modes. To understand and process such phenomena, "divide-and-conquer" is probably the most common strategy to address the problem. In other words, the captured signal is decomposed into signal components for each individual component to be processed. Unfortunately, for signals that are superimposition of non-stationary amplitude-frequency modulated (AM-FM) components, the "divide-and-conquer" strategy is bound to fail, since there is no way to be sure that the decomposed components take on the AM-FM formulations which are necessary for the extraction of their instantaneous frequencies (IFs) and amplitudes (IAs). In this paper, we propose an adaptive signal separation operation (ASSO) for effective and accurate separation of a single-channel blind-source multi-component signal, via introducing a time-varying parameter that adapts locally to IFs and using linear chirp (linear frequency modulation) signals to approximate components at each time instant. We derive more accurate component recovery formulae based on the linear chirp signal local approximation. In addition, a recovery scheme, together with a ridge detection method, is also proposed to extract the signal components one by one, and the time-varying parameter is updated for each component. The proposed method is suitable for engineering implementation, being capable of separating complicated signals into their components or sub-signals and reconstructing the signal trend directly. Numerical experiments on synthetic and real-world signals are presented to demonstrate our improvement over the previous attempts.

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arXiv2022

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

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.

math.NA↗

arXiv2021

A Chirplet Transform-based Mode Retrieval Method for Multicomponent Signals with Crossover Instantaneous Frequencies

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 one and 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

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arXiv2020

Time-Scale-Chirp_rate Operator for Recovery of Non-stationary Signal Components with Crossover Instantaneous Frequency Curves

The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly cross-over instantaneous frequency (IF) curves from a multi-component blind-source signal. The main idea is to incorporate a chirp rate parameter with the time-scale continuous wavelet-like transformation, by considering the quadratic phase representation of the signal components. Hence-forth, even if two IF curves cross, the two corresponding signal components can still be separated and recovered, provided that their chirp rates are different. In other words, signal components with the same IF value at any time instant could still be recovered. To facilitate our presentation, we introduce the notion of time-scale-chirp_rate (TSC-R) recovery transform or TSC-R recovery operator to develop a TSC-R theory for the 3-dimensional space of time, scale, chirp rate. Our theoretical development is based on the approximation of the non-stationary signal components with linear chirps and applying the proposed adaptive TSC-R transform to the multi-component blind-source signal to obtain fairly accurate error bounds of IF estimations and signal components recovery. Several numerical experimental results are presented to demonstrate the out-performance of the proposed method over all existing time-frequency and time-scale approaches in the published literature, particularly for non-stationary source signals with crossover IFs.

math.NA↗

arXiv2020

Signal Separation Based on Adaptive Continuous Wavelet Transform and Analysis

Recently the synchrosqueezed transform (SST) was developed as an empirical mode decomposition (EMD)-like tool to enhance the time-frequency resolution and energy concentration of a multi-component 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 multi-component 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 on some variant of the short-time Fourier transform. In the present paper, we propose a direct method of signal separation based on the adaptive continuous wavelet-like transform (CWLT) by introducing two models of the adaptive CWLT-based approach for signal separation: the sinusoidal signal-based model and the linear chirp-based model, which are derived respectively from sinusoidal signal approximation and the linear chirp approximation at any time instant. A more accurate component recovery formula is derived from linear chirp local approximation. We present the theoretical analysis of our approach. For each model, we establish the error bounds for IF estimation and component recovery.

math.NA↗

arXiv2020

Analysis of an Adaptive Short-Time Fourier Transform-Based Multicomponent Signal Separation Method Derived from Linear Chirp Local Approximation

The synchrosqueezing transform (SST) has been developed as a powerful EMD-like tool for instantaneous frequency (IF) estimation and component separation of non-stationary multicomponent signals. Recently, a direct method of the time-frequency approach, called signal separation operation (SSO), was introduced to solving the problem of 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). In addition, SSO is simple: the IF of a component is estimated by a time-frequency ridge of the SSO plane; and this component is recovered by simply plugging the time-frequency ridge to the SSO operation. In recent paper "Direct signal separation via extraction of local frequencies with adaptive time-varying parameters", after showing that the SSO operation is related to the adaptive short-time Fourier transform (STFT), the authors obtained a more accurate component recovery formula derived from the linear chirp (also called linear frequency modulation signal) approximation at any local time and they also proposed a recovery scheme to extract the signal components one by one with the time-varying window updated for each component. However the theoretical analysis of the recovery formula derived from linear chirp local approximation has not been studied there. In this paper, we carry out such analysis and obtain error bounds for IF estimation and component recovery. These results provide a mathematical guarantee to the proposed adaptive STFT-based non-stationary multicomponent signal separation method.

math.NA↗

arXiv2020

Analysis of Adaptive Synchrosqueezing Transform with a Time-varying Parameter

The synchrosqueezing transform (SST) was developed recently to separate the components of non-stationary multicomponent signals. The continuous wavelet transform-based SST (WSST) reassigns the scale variable of the continuous wavelet transform of a signal to the frequency variable and sharpens the time-frequency representation. The WSST with a time-varying parameter, called the adaptive WSST, was introduced very recently in the paper "Adaptive synchrosqueezing transform with a time-varying parameter for non-stationary signal separation". The well-separated conditions of non-stationary multicomponent signals with the adaptive WSST and a method to select the time-varying parameter were proposed in that paper. In addition, simulation experiments in that paper show that the adaptive WSST is very promising in estimating the instantaneous frequency of a multicomponent signal, and in accurate component recovery. However the theoretical analysis of the adaptive WSST has not been studied. In this paper, we carry out such analysis and obtain error bounds for component recovery with the adaptive WSST and the 2nd-order adaptive WSST. These results provide a mathematical guarantee to non-stationary multicomponent signal separation with the adaptive WSST.

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arXiv2019

Adaptive Short-time Fourier Transform and Synchrosqueezing Transform for Non-stationary Signal Separation

The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier transform (STFT) with a time-varying parameter, called the adaptive STFT. Based on the local approximation of linear frequency modulation mode, we analyze the well-separated condition of non-stationary multicomponent signals using the adaptive STFT with the Gaussian window function. We propose the STFT-based synchrosqueezing transform (FSST) with a time-varying parameter, named the adaptive FSST, to enhance the time-frequency concentration and resolution of a multicomponent signal, and to separate its components more accurately. In addition, we also propose the 2nd-order adaptive FSST to further improve the adaptive FSST for the non-stationary signals with fast-varying frequencies. Furthermore, we present a localized optimization algorithm based on our well-separated condition to estimate the time-varying parameter adaptively and automatically. Simulation results on synthetic signals and the bat echolocation signal are provided to demonstrate the effectiveness and robustness of the proposed method.

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arXiv2019

Adaptive Synchrosqueezing Transform with a Time-Varying Parameter for Non-stationary Signal Separation

The continuous wavelet transform (CWT) is a linear time-frequency representation and a powerful tool for analyzing non-stationary signals. The synchrosqueezing transform (SST) is a special type of the reassignment method which not only enhances the energy concentration of CWT in the time-frequency plane, but also separates the components of multicomponent signals. The "bump wavelet" and Morlet's wavelet are commonly used continuous wavelets for the wavelet-based SST. There is a parameter in these wavelets which controls the widths of the time-frequency localization window. In most literature on SST, this parameter is a fixed positive constant. In this paper, we consider the CWT with a time-varying parameter (called the adaptive CWT) and the corresponding SST (called the adaptive SST) for instantaneous frequency estimation and multicomponent signal separation. We also introduce the 2nd-order adaptive SST. We analyze the separation conditions for non-stationary multicomponent signals with the local approximation of linear frequency modulation mode. We derive well-separated conditions of a multicomponent signal based on the adaptive CWT. We propose methods to select the time-varying parameter so that the corresponding adaptive SSTs of the components of a multicomponent signal have sharp representations and are well-separated, and hence the components can be recovered more accurately. We provide comparison experimental results to demonstrate the efficiency and robustness of the proposed adaptive CWT and adaptive SST in separating components of multicomponent signals with fast varying frequencies.

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arXiv2019

Two-Sample Test Based on Classification Probability

Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of classification probabilities from a classifier trained from the samples, a test statistic is proposed. We explain why such a test can be a powerful test and compare its performance in terms of the power and efficiency with those of some other recently proposed tests with simulation and real-life data. The test proposed is nonparametric and can be applied to complex and high dimensional data wherever there is a classifier that provides consistent estimate of the classification probability for such data.

math.ST↗

arXiv2018

Analysis of Adaptive Short-time Fourier Transform-based Synchrosqueezing Transform

Recently the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method for instantaneous frequency estimation and component separation 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. Very recently the FSST with a time-varying parameter, called the adaptive FSST, was introduced. The simulation experiments show that the adaptive FSST is very promising in instantaneous frequency estimation of the component of a multicomponent signal, and in accurate component recovery. However the theoretical analysis of the adaptive FSST has not been carried out. In this paper, we study the theoretical analysis of the adaptive FSST and obtain the error bounds for the instantaneous frequency estimation and component recovery with the adaptive FSST and the 2nd-order adaptive FSST.

math.NA↗

arXiv2015

Symmetric Canonical Quincunx Tight Framelets with High Vanishing Moments and Smoothness

We propose an approach to construct a family of two-dimensional compactly supported real-valued symmetric quincunx tight framelets $\{ϕ; ψ_1,ψ_2,ψ_3\}$ in $L_2(R^2)$ with arbitrarily high orders of vanishing moments. Such symmetric quincunx tight framelets are associated with quincunx tight framelet filter banks $\{a;b_1,b_2,b_3\}$ having increasing orders of vanishing moments and enjoying the additional double canonical properties: \[ b_1(k_1,k_2)=(-1)^{1+k_1+k_2} a(1-k_1,-k_2), b_3(k_1,k_2)=(-1)^{1+k_1+k_2} b_2(1-k_1,-k_2). \] For a low-pass filter $a$ which is not a quincunx orthonormal wavelet filter, we show that a quincunx tight framelet filter bank $\{a;b_1,\ldots,b_L\}$ with $b_1$ taking the above canonical form must have $L\ge 3$ high-pass filters. Thus, our family of symmetric double canonical quincunx tight framelets has the minimum number of generators. Numerical calculation indicates that this family of symmetric double canonical quincunx tight framelets can be arbitrarily smooth. Using one-dimensional filters having linear-phase moments, in this paper we also provide a second approach to construct multiple canonical quincunx tight framelets with symmetry. In particular, the second approach yields a family of $6$-multiple canonical real-valued quincunx tight framelets in $L_2(R^2)$ and a family of double canonical complex-valued quincunx tight framelets in $L_2(R^2)$ such that both of them have symmetry and arbitrarily increasing orders of smoothness and vanishing moments. Several examples are provided to illustrate our general construction and theoretical results on canonical quincunx tight framelets in $L_2(R^2)$ with symmetry, high vanishing moments, and smoothness. Symmetric quincunx tight framelets constructed by both approaches in this paper are of particular interest for their applications in computer graphics and image processing.

cs.IT↗