scholarly journals Functions of banded Hermitian block Toeplitz matrices in signal processing

2007 ◽  
Vol 422 (2-3) ◽  
pp. 788-807 ◽  
Author(s):  
Jesús Gutiérrez-Gutiérrez ◽  
Pedro M. Crespo ◽  
Albrecht Böttcher
Keyword(s):  
Signal Processing ◽  
Toeplitz Matrices ◽  
Block Toeplitz Matrices

scholarly journals Applications of the Periodogram Method for Perturbed Block Toeplitz Matrices in Statistical Signal Processing

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 582
Author(s):  
Jesús Gutiérrez-Gutiérrez ◽  
Xabier Insausti ◽  
Marta Zárraga-Rodríguez
Keyword(s):  
Signal Processing ◽  
Parameter Estimation ◽  
Moving Average ◽  
Toeplitz Matrices ◽  
Estimation Method ◽  
Cholesky Decomposition ◽  
Statistical Signal Processing ◽  
Correlation Matrices ◽  
Vector Autoregressive ◽  
Block Toeplitz Matrices

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.

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