发帖
雷达卡
摘要翻译：
奇异谱分析(SSA)或奇异值分解(SVD)常用于对单变量时间序列进行去噪或研究其谱分布。这两种技术都依赖于将信号嵌入到延迟信号中后估计的相关矩阵的特征分解。在这一工作中，我们证明了特征向量可以用来计算一组滤波器的系数，这些滤波器构成一个滤波器组。导出了这些滤波器的性质。特别地，我们表明它们的输出可以根据它们的频率响应进行分组。此外，每个频率响应最大值处的频率和相应的特征值可以提供时间序列的功率谱估计。两个不同的应用说明了如何将这两个特性应用于分析宽带信号，以获得窄带信号或推断它们的频率占用。
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英文标题：
《On the use of Singular Spectrum Analysis》
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作者：
A.M. Tom\'e, D. Malafaia, A.R. Teixeira, E.W. Lang
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最新提交年份：
2018
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分类信息：
一级分类：Electrical Engineering and Systems Science 电气工程与系统科学
二级分类：Signal Processing 信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix estimated after embedding the signal into its delayed coordi- nates. In this work we show that the eigenvectors can be used to calculate the coefficients of a set of filters which form a filter bank. The properties of these filters are derived. In particular we show that their outputs can be grouped according to their frequency response. Furthermore, the fre- quency at the maximum of each frequency response and the corresponding eigenvalue can provide a power spectrum estimation of the time series. Two different applications illustrate how both characteristics can be applied to analyze wideband signals in order to achieve narrow-band signals or to infer their frequency occupation.
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PDF链接：
https://arxiv.org/pdf/1807.10679
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