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Jiecheng Chen

Publications and source records attributed to Jiecheng Chen.

13 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.

eess.SP↗
arXiv2026

Almost sharp variational estimates for discrete truncated operators of Stein-Wainger type

We establish $r$-variational estimates for discrete truncated Stein-Wainger type operators on $\ell^p$ for $1<p<\infty$. Notably, these estimates are sharp and enhance the results obtained by Krause and Roos (J. Eur. Math. Soc. 2022, J. Funct. Anal. 2023), up to a logarithmic loss related to the scale. On the other hand, as $r$ approaches infinity, the consequences align with the estimates proved by Krause and Roos. Moreover, for the case of quadratic phases, we remove this logarithmic loss with respect to the scale in two and higher dimensions, at the cost of increasing $p$ slightly.

math.CA↗
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.

eess.SP↗
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.

eess.SP↗
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.

eess.SP↗
arXiv2024

A maximal oscillatory operator on compact manifolds

This is a continuation of our previous research about an oscillatory integral operator $T_{α, β}$ on compact manifolds $\mathbb{M}$. We prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator $T^{*}_{α, β}$ for all $0<p<1$. As applications, we first prove the sharp $H^{p}$-$L^{p,\infty}$ boundedness on the maximal operator corresponding to the Riesz means $I_{k,α}(|\mathcal{L}|)$ associated with the Schrödinger type group $e^{is\mathcal{L}^{α/2}}$ and obtain the almost everywhere convergence of $I_{k,α}(|\mathcal{L}|)f(x,t)\to f(x)$ for all $f\in H^{p}$. Also, we are able to obtain the convergence speed of a combination operator from the solutions of the Cauchy problem of fractional Schrödinger equations. All results are even new on the n-torus $T^{n}$.

math.AP↗
arXiv2022

$L^p(\mathbb{R}^d)$ boundedness for the Calderón commutator with rough kernel

Let $k\in\mathbb{N}$, $Ω$ be homogeneous of degree zero, integrable on $S^{d-1}$ and have vanishing moment of order $k$, $a$ be a function on $\mathbb{R}^d$ such that $\nabla a\in L^{\infty}(\mathbb{R}^d)$, and $T_{Ω,\,a;k}$ be the $d$-dimensional Calderón commutator defined by $$T_{Ω,\,a;k}f(x)={\rm p.\,v.}\int_{\mathbb{R}^d}\frac{Ω(x-y)}{|x-y|^{d+k}}\big(a(x)-a(y)\big)^kf(y){d}y.$$ In this paper, the authors prove that if $$\sup_{ζ\in S^{d-1}}\int_{S^{d-1}}|Ω(θ)|\log ^β \big(\frac{1}{|θ\cdotζ|}\big)dθ<\infty,$$ with $β\in(1,\,\infty]$, then for $\frac{2β}{2β-1}<p<2β$, $T_{Ω,\,a;\,k}$ is bounded on $L^p(\mathbb{R}^d)$.

math.CA↗
arXiv2022

Sparse Representations of Solutions to a class of Random Boundary Value Problems

We introduce certain sparse representation methods, named as stochastic pre-orthogonal adaptive Fourier decomposition 1 and 2 (SPOAFD1 and SPOAFD2) to solve the Dirichlet boundary value problem and the Cauchy initial value problem of random data. To solve the stochastic boundary value problems the sparse representation is, as the initial step, applied to the random boundary data. Due to the semigroup property of the Poisson and the heat kernel, each entry of the expanding series can be lifted up to compose a solution of the Dirichlet and the Cauchy initial value problem, respectively. The sparse representation gives rise to analytic as well as numerical solutions to the problems with high efficiency.

math.NA↗
arXiv2020

Characterization of boundedness on weighted modulation spaces of $τ$-Wigner distributions

This paper is devoted to give several characterizations on a more general level for the boundedness of $τ$-Wigner distributions acting from weighted modulation spaces to weighted modulation and Wiener amalgam spaces. As applications, sharp exponents are obtained for the boundedness of $τ$-Wigner distributions on modulation spaces with power weights. We also recapture the main theorems of Wigner distribution obtained in \cite{CorderoNicola2018IMRNI,Cordero2020a}. As consequences, the characterizations of the boundedness on weighted modulation spaces of several types of pseudodifferential operators are established. In particular, we give the sharp exponents for the boundedness of pseudodifferential operators with symbols in Sjöstrand's class and the corresponding Wiener amalgam spaces.

math.FA↗
arXiv2018

Weighted estimates for the Calderón commutator

In this paper, the authors establish some weighted estimates for the Calderón commutator defined by \begin{eqnarray*} &&\mathcal{C}_{m+1,\,A}(a_1,\dots,a_{m};f)(x) &&\quad={\rm p.\,v.}\,\int_{\mathbb{R}}\frac{P_2(A;\,x,\,y)\prod_{j=1}^m(A_j(x)-A_j(y))}{(x-y)^{m+2}}f(y){\rm d}y, \end{eqnarray*} with $P_2(A;\,x,\,y)=A(x)-A(y)-A'(y)(x-y)$. Dominating this operator by multi(sub)linear sparse operators, the authors establish the weighted bounds from $L^{p_1}(\mathbb{R},w_1)$ $\times\dots\times L^{p_m}(\mathbb{R},w_m)$ to $L^{p}(\mathbb{R},ν_{\vec{w}})$, with $p_1,\dots,p_m \in (1,\,\infty)$, $1/p=1/p_1+\dots+1/p_m$, and $\vec{w}=(w_1,\,\dots,\,w_m)\in A_{\vec{P}}(\mathbb{R}^{m+1})$. The authors also obtain the weighted weak type endpoint estimates for this operator

math.CA↗
arXiv2016

Weighted vector-valued bounds for a class of multilinear singular integral operators

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\,\mathbb{R}^n,w_1)\times\dots\times L^{p_m}(l^{q_m};\,\mathbb{R}^n,w_m)$ to $L^{p}(l^q;\,\mathbb{R}^n,ν_{\vec{w}})$, with $p_1,\dots,p_m\in (1,\,\infty)$ and $1/p=1/p_1+\dots+1/p_m$ and $\vec{w}$ is a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators.

math.CA↗
arXiv2016

Characterization of Some Properties on Weighted Modulation Spaces

In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution inequalities and embedding on weighted modulation and Wiener amalgam spaces are obtained. These applications improve and extend many known results.

math.CA↗