TY - GEN
T1 - An extended displacement operator for weakly structured covariance matrices
AU - Desbouvries, F.
AU - Gueguentt, C.
N1 - Publisher Copyright:
© 1992 IEEE.
PY - 1992/1/1
Y1 - 1992/1/1
N2 - The Gohberg-Semencul formula is an explicit expression of the inverse of a Toeplitz matrix in terms of a reduced number of parameters which happen to be the forward and backward autoregressive parameters. It has been nicely understood in terms of displacement ranks. With the help of a new displacement operator, it is shown that this two-Term formula remains valid in the general positive definite case, provided that the shifted predictors are now associated with the successive principal submatrices. Besides, this formula induces a general relationship among forward and backward predictors.
AB - The Gohberg-Semencul formula is an explicit expression of the inverse of a Toeplitz matrix in terms of a reduced number of parameters which happen to be the forward and backward autoregressive parameters. It has been nicely understood in terms of displacement ranks. With the help of a new displacement operator, it is shown that this two-Term formula remains valid in the general positive definite case, provided that the shifted predictors are now associated with the successive principal submatrices. Besides, this formula induces a general relationship among forward and backward predictors.
U2 - 10.1109/ICASSP.1992.226668
DO - 10.1109/ICASSP.1992.226668
M3 - Conference contribution
AN - SCOPUS:85019553755
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 21
EP - 24
BT - ICASSP 1992 - 1992 International Conference on Acoustics, Speech, and Signal Processing
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 1992
Y2 - 23 March 1992 through 26 March 1992
ER -