Statistics and Its Interface

Volume 10 (2017)

Number 1

Asymptotic extraction of common signal subspaces from perturbed signals

Pages: 27 – 32

DOI: https://dx.doi.org/10.4310/SII.2017.v10.n1.a3

Authors

Vladimir Nekrutkin (Department of Mathematics, St. Petersburg State University, St. Petersburg, Russia)

Irina Vasilinetc (Algorithmic Biology Lab, St. Petersburg Academic University, St. Petersburg, Russia)

Abstract

Signal subspaces extracted by Singular Value Decomposition of signal matrices are used in many methods of signal processing. General approach to asymptotic proximity of unperturbed and perturbed signal subspaces is discussed in Nekrutkin 2010, SII, v. 3, 297–319. These theoretical results are illustrated by several examples related to onedimensional signals and the corresponding Hankel matrices.

In this paper we apply this approach to the multidimensional signals and block-Hankel matrices. More precisely, we suppose that each coordinate of a multidimensional signal produces the same signal subspace. For such signals, we suggest the solution for asymptotic extraction of this subspace from the perturbed multidimensional signal series.

A similar procedure is already used in atmosphere sciences to incorporate both spatial and temporal correlations in multidimensional data.

Keywords

signal subspace methods, perturbation expansion, asymptotic analysis, multidimensional signals

2010 Mathematics Subject Classification

Primary 65F30, 65G99. Secondary 65F15.

Published 27 September 2016