A derivation of the Gohberg-Semencul relation (signal analysis)

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.<
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