摘要翻译：
在Nekrutkin2010,SII,V.3,297--319中已经概述了利用奇异谱分析（简称SSA）从扰动信号中渐近提取信号序列的一般理论方法。在本文中，我们考虑了这种分析应用于指数信号和正弦噪声的例子。证明了当信号迅速趋于无穷大时，当序列长度趋于无穷大时，所谓的SSA重构误差并不一致地趋于零。更确切地说，在这种情况下，误差序列的最后一项的任何有限数目都不趋向于任何有限或无限的值。相反，对于指数信号以上有界的“离散化”格式，误差级数的所有元素趋于零。这一结果表明，离散化模型可以作为一种有效的工具，在理论SSA考虑的信号越来越多。
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英文标题：
《Two asymptotic approaches for the exponential signal and harmonic noise
  in Singular Spectrum Analysis》
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作者：
Elizaveta Ivanova and Vladimir Nekrutkin
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最新提交年份：
2017
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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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一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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英文摘要：
  The general theoretical approach to the asymptotic extraction of the signal series from the perturbed signal with the help of Singular Spectrum Analysis (briefly, SSA) was already outlined in Nekrutkin 2010, SII, v. 3, 297--319.   In this paper we consider the example of such an analysis applied to the increasing exponential signal and the sinusoidal noise. It is proved that if the signal rapidly tends to infinity, then the so-called reconstruction errors of SSA do not uniformly tend to zero as the series length tends to infinity. More precisely, in this case any finite number of last terms of the error series do not tend to any finite or infinite values.   On the contrary, for the "discretization" scheme with the bounded from above exponential signal, all elements of the error series tend to zero.   This effect shows that the discretization model can be an effective tool in the theoretical SSA considerations with increasing signals.
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PDF链接：
https://arxiv.org/pdf/1709.08651