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Exponential data fitting using multilinear algebra: the single‐channel and multi‐channel case
Author(s) -
Papy J. M.,
De Lathauwer L.,
Van Huffel S.
Publication year - 2005
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.453
Subject(s) - multilinear algebra , singular value decomposition , multilinear map , toeplitz matrix , mathematics , hankel matrix , matrix (chemical analysis) , matrix pencil , algorithm , generalization , singular value , channel (broadcasting) , exponential function , matrix decomposition , subspace topology , pencil (optics) , tensor (intrinsic definition) , eigenvalues and eigenvectors , algebra over a field , mathematical analysis , computer science , pure mathematics , computer network , materials science , physics , quantum mechanics , division algebra , composite material , filtered algebra , mechanical engineering , engineering
Abstract There is a wide variety of signal processing applications in which the data are assumed to be modelled as a sum of exponentially damped sinusoids. Many subspace‐based approaches (such as ESPRIT, matrix pencil, Prony, etc.) aim to estimate the parameters of this model. Typically, the data are arranged in Toeplitz or Hankel matrices and suitable parameter estimates are obtained via a truncated singular value decomposition (SVD) of the data matrix. It is shown that the parameter accuracy may be improved by arranging single‐channel or multi‐channel data in a higher‐order tensor and estimating the model parameters via a multilinear generalization of the SVD. The algorithm is presented and its performance is illustrated by means of simulations. Copyright © 2005 John Wiley & Sons, Ltd.