Applications of the periodogram method for perturbed block toeplitz satrices in statistical signal processing

Gutiérrez-Gutiérrez, J. (Jesús); Insausti-Sarasola, X. (Xabier); Zárraga-Rodríguez, M. (Marta de)

Authors:

Gutiérrez-Gutiérrez, J. (Jesús)

Insausti-Sarasola, X. (Xabier)

Zárraga-Rodríguez, M. (Marta de)

Keywords:

Parameter estimation
Periodogram method for perturbed block Toeplitz matrices
The Cholesky decomposition
Vector autoregressive (VAR) processes
Vector moving average (VMA) processes

Issue Date:

2020

Publisher:

MDPI

ISSN:

2227-7390

Note:

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution

Citation:

Gutiérrez-Gutiérrez, J. (Jesús); Insausti-Sarasola, X. (Xabier); Zárraga-Rodríguez, M. (Marta). "Applications of the periodogram method for perturbed block toeplitz satrices in statistical signal processing". Mathematics. 8 (4), 2020, 582

Abstract

In this paper, we combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition to give a parameter estimation method for any perturbed vector autoregressive (VAR) or vector moving average (VMA) process, when we only know a perturbed version of the sequence of correlation matrices of the process. In order to combine the periodogram method for perturbed block Toeplitz matrices with the Cholesky decomposition, we first need to generalize a known result on the Cholesky decomposition of Toeplitz matrices to perturbed block Toeplitz matrices.

URI:

https://hdl.handle.net/10171/65220

DOI:

10.3390/math8040582

Appears in Collections:

DA - TECNUN - Ingeniería Biomédica y Ciencias - Artículos de revista

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