2017/09/22 by Elizaveta Ivanova, Ivanova, Elizaveta, В. В. Некруткин +1
Engineering · Mathematics · #Advanced Electrical Measurement Techniques #FOS: Electrical engineering #FOS: Mathematics #Machine Fault Diagnosis Techniques #Numerical Analysis (math.NA) #Signal Processing (eess.SP) #Statistical and numerical algorithms #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1709.08651
openalex publication_date 2017/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The general theoretical approach to the asymptotic extraction of the signal\nseries from the perturbed signal with the help of Singular Spectrum Analysis\n(briefly, SSA) was already outlined in Nekrutkin 2010, SII, v. 3, 297--319.\n In this paper we consider the example of such an analysis applied to the\nincreasing exponential signal and the sinusoidal noise. It is proved that if\nthe signal rapidly tends to infinity, then the so-called reconstruction errors\nof SSA do not uniformly tend to zero as the series length tends to infinity.\nMore precisely, in this case any finite number of last terms of the error\nseries do not tend to any finite or infinite values.\n On the contrary, for the "discretization" scheme with the bounded from above\nexponential signal, all elements of the error series tend to zero.\n This effect shows that the discretization model can be an effective tool in\nthe theoretical SSA considerations with increasing signals.\n