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Convolution Type of Metaplectic Cohen's Distribution Time-Frequency analysis Theory, Method and Technology

IEEE Transactions on Information Theory 2025年第3期71卷 2292-2314页

作者： Cui, Manjun Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng Nanjing University of Information Science and Technology School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing210044 China Nanjing University of Information Science and Technology School of Mathematics and Statistics Nanjing210044 China Shanghai Jiao Tong University Key Laboratory of System Control and Information Processing Ministry of Education Shanghai200240 China Hainan Normal University Key Laboratory of Computational Science and Application of Hainan Province Haikou571158 China Nanjing University of Information Science and Technology School of Remote Sensing and Geomatics Engineering Nanjing210044 China

The conventional Cohen's distribution can't meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for non-stationary signal fractional domain time-frequency analysis. In this paper, we embark on blending time-frequency operators and coordinate operator fractionizations to formulate the definition of the joint fractionizations metaplectic Wigner distribution (JFMWD), based on which we integrate the generalized metaplectic convolution to address the unified representation issue of the convolution type of metaplectic Cohen's distribution (CMCD), whose special cases and essential properties are also derived. We blend Wiener filter principle and fractional domain filter mechanism of the metaplectic transform to design the least-squares adaptive filter method in the JFMWD domain, giving birth to the least-squares adaptive filter-based CMCD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error (MSE) denoising in Wigner distribution domain. We discuss the optimal symplectic matrices selection strategy of the proposed adaptive CMCD through the minimum MSE minimization modeling and solving. Some examples are also carried out to demonstrate that the proposed filtering method outperforms some state-of-the-arts including the classical Gaussian filter, the Cohen's distribution filtering methods with fixed kernel functions, the classical Wiener filter, the adaptive generalized linear canonical convolution-based filtering method, the adaptive Cohen's distribution filtering method, the adaptive JFMWD-based Cohen's distribution filtering method, and the adaptive generalized metaplectic convolution-based Cohen's distribution filtering method in noise suppression. © 1963-2012 IEEE.

关键词： Adaptive filtering

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Strong Time-Periodic Solutions to the 3d Oceanic Primitive Equations with the Gent-Mcwilliams-Redi Eddy Parametrization Model and Arbitrary Large Outer Forces

SSRN

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SSRN 2025年

作者： Zhang, Jie Liu, Wenjun School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

To capture the effect of mesoscale eddies on oceanic temperature and salinity, we take the Gent-McWilliams-Redi eddy parametrization model into account in an ocean model with outer forces consisting of the 3D primitive equations and a set of advection-diffusion equations describing the oceanic tracers of temperature and salinity. The existence of strong time-periodic ($T$-periodic) solutions for this model is established under three time-periodic outer forces without any smallness conditions, provided that the density function for pressure, temperature and salinity satisfies the certain regularity assumption. Firstly, we prove the existence of a weak $T$-periodic solution relying on the Faedo-Galerkin method, Brouwer's fixed-point theorem and a priori bounds. Secondly, we prove the global well-posedness of strong solutions for arbitrary large outer forces and initial data that are in appropriately chosen function classes. Finally, we adopt the method of the weak-strong uniqueness to obtain a strong $T$-periodic solution for this model. © 2025, The Authors. All rights reserved.

关键词： Fixed point arithmetic

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Dynamic and static Lagrange multiplier μ based Bayesian CP factorization with orthogonal factors: Theory and applications

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Signal Processing 2025年 236卷

作者： Zhou, Jing Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province and Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Hainan Normal University Haikou571158 China

The existing μ-Singular Value Decomposition (μ-SVD) denoising algorithm is capable of extracting gear fault information under strong noise conditions. However, this algorithm is only applicable to two-dimensional real-valued data and lacks a mechanism for implementing Automatic Rank Determination (ARD) in high-dimensional data. In this paper, a Bayesian and Tensor treatment of μ-SVD is employed to enable ARD. To further investigate the impact of the Lagrange multiplier μ on the proposed μ-variational Bayesian (μ-VB) algorithm, we examine its performance from both static and dynamic perspectives. Simulation results demonstrate that the μ-VB algorithm achieves ARD and performs well in noise reduction. Further the μ-VB algorithm performs better in wireless communication and linear image coding across numerical domains, tensor sizes, orthogonal factors, and μ settings. © 2025 Elsevier B.V.

关键词： Tensors

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Graph Chirp Signal and Graph Fractional Vertex-Frequency Energy Distribution

arXiv

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arXiv 2025年

作者： Cui, Manjun Zhang, Zhichao School of Mathematics and Statistics The Center for Applied Mathematics of Jiangsu Province The Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai Jiao Tong University Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Hainan Normal University Haikou571158 China

Graph signal processing (GSP) has emerged as a powerful framework for analyzing data on irregular domains. In recent years, many classical techniques in signal processing (SP) have been successfully extended to GSP. Among them, chirp signals play a crucial role in various SP applications. However, graph chirp signals have not been formally defined despite their importance. Here, we define graph chirp signals and establish a comprehensive theoretical framework for their analysis. We propose the graph fractional vertex-frequency energy distribution (GFED), which provides a powerful tool for processing and analyzing graph chirp signals. We introduce the general fractional graph distribution (GFGD), a generalized vertex-frequency distribution, and the reduced interference GFED, which can suppress cross-term interference and enhance signal clarity. Furthermore, we propose a novel method for detecting graph signals through GFED domain filtering, facilitating robust detection and analysis of graph chirp signals in noisy environments. Moreover, this method can be applied to real-world data for denoising more effective than some state-of-the-arts, further demonstrating its practical significance. Copyright © 2025, The Authors. All rights reserved.

关键词： Wiener filtering

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Brain MRIs classification based on 2D SWD-MF-DFA

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Journal of Neuroscience Methods 2025年 421卷 110468页

作者： Wang, Jing Wu, Xinpei Wang, Haozhe Wang, Jian School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044 China Reading Academy Nanjing University of Information Science and Technology Nanjing 210044 China Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing 210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing 210044 China

Background: To improve imaging classification accuracy, we modify the traditional 2D multifractal trend fluctuation analysis (MF-DFA) method to better preserve local feature values. Inspired by MF-DFA, we develop a novel method for extracting eigenvalues, enhancing the precision of imaging analysis. New method: In this paper, we propose an enhanced algorithm building upon the traditional 2D MF-DFA. Our approach introduces a 2D sliding window (SWD) technique for feature value extraction. Initially, the local generalized Hurst index of the imaging is derived using the SWD algorithm, based on MF-DFA principles. Subsequently, the generalized Hurst index is recalculated for the digital matrix formed by these local Hurst indexes. These vectors are then input into a support vector machine (SVM) for classification. This methodology seeks to refine the traditional 2D MF-DFA by more effectively preserving local feature values in imaging. Results: The classification accuracy of the SWD eigenvalue extraction method based on 2D MF-DFA reaches 91.54%. Comparison with existing methods: We employ brain magnetic resonance imaging (MRI) data sets to evaluate the efficacy of both the conventional 2D MF-DFA method and our proposed feature value extraction technique. Both methods are applied alongside a SVM for classification. The findings reveal that the conventional 2D MF-DFA method yields a classification accuracy of 59.40%, while our SWD feature value extraction method attains a classification accuracy of 91.54%. Conclusion: This substantial performance enhancement underscores the superiority of the SWD approach over the conventional method. © 2025 Elsevier B.V.

关键词： 2D MF-DFA 2D SWD MRI SVM

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Investigating the sensitivity of nanofluid flow around a cylindrical disk: A study of Walter's B nanofluid using response surface methodology and artificial neural networks

Journal of Engineering Research (Kuwait)

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Journal of Engineering Research (Kuwait) 2025年

作者： Shafiq, Anum Çolak, Andaç Batur Sindhu, Tabassum Naz Abushal, Tahani A. School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing 210044 China Department of Information Systems and Technologies Niğde Ömer Halisdemir University Niğde 51240 United States Department of Statistics Quaid-I-Azam University Islamabad 44000 Pakistan Department of Mathematical Sciences Umm Al-Qura University Makkah 24382 Saudi Arabia

Modern technology development heavily relies on nanotechnology, which has gained significant attention from researchers in recent years, particularly in finding ways to enhance heat transfer rates. One approach to addressing this issue is to use nanoparticles in host fluids to greatly improve their thermal properties. This study employed response surface methods to investigate the Walter's B nanofluid, incorporating thermophoresis, Brownian diffusion, activation energy, and thermal radiation, using the Buongiorno model to examine nanofluid properties. To reduce the formed system of flow equations into a dimensionless differential form system, appropriate variables were used. In addition, we build a dataset for the proposed multilayer perceptron neural network using the Runge-Kutta fourth-order shooting method. The study analyzed effects of flow variables on the velocity field, temperature field, and species volumetric concentration fields, and probable error correlation coefficients were calculated to evaluate the statistical significance of the parameters. Additionally, a sensitivity analysis was conducted, which showed that with a high thermophoresis number, the Nusselt number is more sensitive. © 2024 The Authors

关键词： Artificial neural networks Brownian motion Response surface methodology (RSM) Sensitivity analysis Thermophoresis Walter's B nanofluid

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Multi-dimensional graph linear canonical transform

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Digital Signal Processing: A Review Journal 2025年 165卷

作者： Li, Na Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing 210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai 200240 China Key Laboratory of Computational Science and Application of Hainan Province Haikou 571158 China

Multi-dimensional (M-D) graph signals represent fundamental data structures in various practical applications, including digital imaging systems, sensor network telemetry, and meteorological observation records. The development of efficient transformation methodologies for processing such M-D graph signals within the linear canonical transform domain continues to present significant challenges. This paper introduces two novel transforms: the two-dimensional graph linear canonical transform based on central discrete dilated Hermite functions (2-D CDDHFs-GLCT) and the two-dimensional graph linear canonical transform based on chirp multiplication-chirp convolution-chirp multiplication decomposition (2-D CM-CC-CM-GLCT). These foundational constructs are extended to the multi-dimensional domain, resulting in M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analyses reveal that the M-D CM-CC-CM-GLCT algorithm achieves substantial computational complexity reduction compared to its CDDHFs-based counterpart. Numerical simulations further establish that while maintaining comparable additivity performance, the M-D CM-CC-CM-GLCT exhibits enhanced reversibility characteristics. To validate practical applicability, the proposed M-D GLCT framework is implemented in data compression scenarios. Experimental results demonstrating superior algorithmic efficiency and implementation effectiveness compared to multi-dimensional graph fractional Fourier transform. © 2025 Elsevier Inc.

关键词： data compression Graph signal processing Linear canonical transform Multi-dimensional signal processing

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The Optimal Closed-Form Linear Canonical Wigner Distribution 6

The Optimal Closed-Form Linear Canonical Wigner Distribution

引用

6th international Conference on Information Communication and Signal Processing, ICICSP 2023

作者： Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing China

ISBN: (纸本)9798350339994

This study devotes to Heisenberg's uncertainty inequalities under the closed-form instantaneous cross-correlation function Wigner distribution (CICFWD), whose generalizability enables it to be a representative Wigner distribution (WD) in the linear canonical transform (LCT) domain. A relation between the spread in the time-CICFWD domain and the spreads and moments in LCT domains is established. We then obtain two versions of lower bounds on the uncertainty product of spreads in time-CICFWD and LCT-CICFWD domains. The first is the tightest universal lower bound for all signals, and the other is a lower bound for complex-valued signals. As a result, uncertainty principles for the traditional WD are revisited. The optimal LCT free parameters selection problems of the CICFWD are also well-addressed from the perspectives of the highest time-frequency resolution and its best estimation accuracy, respectively. © 2023 IEEE.

关键词： linear canonical Wigner distribution lower bound time-frequency resolution uncertainty principle

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Bifurcation analysis of a diffusive radio-dependent model with spatial memory

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international Journal of Biomathematics 2024年第8期17卷 309-347页

作者： Qi An Xingyu Guo Xuebing Zhang College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044 P.R.China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing 210044 P.R.China

This is an Open Access article published by World Scientific Publishing *** is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0(CC BY-NC-ND)License,which permits use,distribution and reproduction,provided that the original work is properly cited,the use is non-commercial and no modifications or adaptations are *** cognitive abilities of animals,such as memory,have a significant impact on their movement in *** this paper,we consider a radio-dependent model with memorybased diffusion under the conditions of Neumann *** stability of a positive equilibrium and the existence of the Turing-Hopf bifurcation induced by memory diffusion and memory delay are carried out in ***,our findings indicate that with a relatively short average memory period,the large memory diffusion can stabilize an otherwise unstable *** addition,the third-order truncated normal form for the Turing-Hopf bifurcation restricted to the central manifold is derived,which can reveal the generation of some steady-state and time-periodic solutions with spatial *** coefficients within the normal form are systematically determined through matrix operations,and these results can also be applied to other models with memory ***,leveraging the theoretical findings,we elucidated the intricate spatial-temporal dynamics and their associated parameter scopes caused by Turing-Hopf bifurcation through numerical simulations.

关键词： Spatial memory normal form Turing-Hopf bifurcation spatio-temporal patterns periodic solutions

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Qualitative analysis of a Diffusive Predator-prey Model with Nonlcoal Fear Effect

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数学理论与应用 2024年第3期44卷 67-82页

作者： Shen Zhongyuan Zhang Xuebing Li Shunjie Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data AnalysisNanjing 210044China

In this paper,we establish a delayed predator-prey model with nonlocal fear ***,the existence,uniqueness,and persistence of solutions of the model are ***,the local stability,Turing bifurcation,and Hopf bifurcation of the constant equilibrium state are analyzed by examining the characteristic *** global asymptotic stability of the positive equilibrium point is investigated using the Lyapunov function ***,the correctness of the theoretical analysis results is verified through numerical simulations.

关键词： Delay Nonlocal fear effect Global stability Hopf bifurcation

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