Title :
A derivation of the Gohberg-Semencul relation [signal analysis]
Author :
Cernuschi-Frias, Bruno
Author_Institution :
Fac. de Ingenieria, Buenos Aires Univ., Argentina
fDate :
1/1/1991 12:00:00 AM
Abstract :
A simple proof of the Gohberg-Semencul decomposition of the inverse of the correlation matrix of an autoregressive (AR) process is given. The proof is based on the Cholesky decomposition and the centrosymmetric property of symmetric Toeplitz matrices. The Gohberg-Semencul relation is derived in a simple way by doubling the size, but not the order, of the AR process
Keywords :
correlation theory; matrix algebra; signal processing; Cholesky decomposition; Gohberg-Semencul relation; autoregressive process; centrosymmetric property; correlation matrix; signal analysis; symmetric Toeplitz matrices; Delay effects; Equations; Fourier series; Frequency; Matrix decomposition; Sampling methods; Signal analysis; Symmetric matrices; Time measurement; Writing;
Journal_Title :
Signal Processing, IEEE Transactions on
