Short-time variational mode decomposition

IF 3.6 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
Hao Jia , Pengfei Cao , Tong Liang , Cesar F. Caiafa , Zhe Sun , Yasuhiro Kushihashi , Antoni Grau , Yolanda Bolea , Feng Duan , Jordi Solé-Casals
{"title":"Short-time variational mode decomposition","authors":"Hao Jia ,&nbsp;Pengfei Cao ,&nbsp;Tong Liang ,&nbsp;Cesar F. Caiafa ,&nbsp;Zhe Sun ,&nbsp;Yasuhiro Kushihashi ,&nbsp;Antoni Grau ,&nbsp;Yolanda Bolea ,&nbsp;Feng Duan ,&nbsp;Jordi Solé-Casals","doi":"10.1016/j.sigpro.2025.110203","DOIUrl":null,"url":null,"abstract":"<div><div>Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies using Fourier transformations. However, since these transformations span the entire time-domain signal, they are suboptimal for analyzing non-stationary time series.</div><div>We introduce Short-Time Variational Mode Decomposition (STVMD), an innovative extension of VMD that incorporates Short-Time Fourier transform (STFT) to minimize the impact of local disturbances. STVMD segments signals into short time windows and converts these segments into the frequency domain. It then formulates a variational optimization problem to extract band-limited modes representing the windowed data. The optimization aims to minimize the sum of mode bandwidths across the windowed data, extending the cost functions used in VMD and MVMD. Solutions are derived using the alternating direction method of multipliers, ensuring extraction of modes with narrow bandwidths.</div><div>STVMD is divided into dynamic and non-dynamic types, depending on whether central frequencies vary with time. Our experiments show non-dynamic STVMD matches VMD with properly sized time windows, while dynamic STVMD better accommodates non-stationary signals through reduced mode function errors and tracking of dynamic frequencies. This effectiveness is validated using steady-state visual-evoked potentials in electroencephalogram signals.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"238 ","pages":"Article 110203"},"PeriodicalIF":3.6000,"publicationDate":"2025-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Signal Processing","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165168425003172","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0

Abstract

Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies using Fourier transformations. However, since these transformations span the entire time-domain signal, they are suboptimal for analyzing non-stationary time series.
We introduce Short-Time Variational Mode Decomposition (STVMD), an innovative extension of VMD that incorporates Short-Time Fourier transform (STFT) to minimize the impact of local disturbances. STVMD segments signals into short time windows and converts these segments into the frequency domain. It then formulates a variational optimization problem to extract band-limited modes representing the windowed data. The optimization aims to minimize the sum of mode bandwidths across the windowed data, extending the cost functions used in VMD and MVMD. Solutions are derived using the alternating direction method of multipliers, ensuring extraction of modes with narrow bandwidths.
STVMD is divided into dynamic and non-dynamic types, depending on whether central frequencies vary with time. Our experiments show non-dynamic STVMD matches VMD with properly sized time windows, while dynamic STVMD better accommodates non-stationary signals through reduced mode function errors and tracking of dynamic frequencies. This effectiveness is validated using steady-state visual-evoked potentials in electroencephalogram signals.
短时变分模态分解
变分模态分解(VMD)及其扩展如多元模态分解(MVMD)利用傅里叶变换将信号分解为具有窄中心频率的带限模态集合。然而,由于这些变换跨越整个时域信号,它们对于分析非平稳时间序列是次优的。我们引入短时变分模态分解(STVMD),这是VMD的一种创新扩展,它结合了短时傅里叶变换(STFT)来最小化局部干扰的影响。STVMD将信号分割成短时间窗口,并将其转换为频域。然后,提出了一个变分优化问题来提取表示窗口数据的带限模式。优化的目标是最小化窗口数据的模式带宽之和,扩展了VMD和MVMD中使用的代价函数。利用乘法器的交替方向法推导了解,保证了窄带宽模式的提取。根据中心频率是否随时间变化,STVMD分为动态和非动态类型。我们的实验表明,非动态STVMD与适当大小的时间窗的VMD相匹配,而动态STVMD通过减小模态函数误差和跟踪动态频率,更好地适应非平稳信号。使用脑电图信号中的稳态视觉诱发电位验证了这种有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Signal Processing
Signal Processing 工程技术-工程:电子与电气
CiteScore
9.20
自引率
9.10%
发文量
309
审稿时长
41 days
期刊介绍: Signal Processing incorporates all aspects of the theory and practice of signal processing. It features original research work, tutorial and review articles, and accounts of practical developments. It is intended for a rapid dissemination of knowledge and experience to engineers and scientists working in the research, development or practical application of signal processing. Subject areas covered by the journal include: Signal Theory; Stochastic Processes; Detection and Estimation; Spectral Analysis; Filtering; Signal Processing Systems; Software Developments; Image Processing; Pattern Recognition; Optical Signal Processing; Digital Signal Processing; Multi-dimensional Signal Processing; Communication Signal Processing; Biomedical Signal Processing; Geophysical and Astrophysical Signal Processing; Earth Resources Signal Processing; Acoustic and Vibration Signal Processing; Data Processing; Remote Sensing; Signal Processing Technology; Radar Signal Processing; Sonar Signal Processing; Industrial Applications; New Applications.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信