The Euclid algorithm and the fast computation of cross-covariance and autocovariance sequences
- 1 April 1989
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Acoustics, Speech, and Signal Processing
- Vol. 37 (4) , 545-552
- https://doi.org/10.1109/29.17535
Abstract
A simple linear procedure is given to compute the cross-covariance sequence associated with the outputs of two rational digital transfer functions driven by the same white noise sequence. Such a computation often appears in the study of digital filters, in Wiener filtering, in noise variance estimation, in the study of low-order approximations, and in the study of multichannel systems. A fast algorithm based on the Euclid algorithm is introduced to solve the linear system of equations involved in the computation, and a detailed analysis of the matrix is given. The special case of the autocovariance computation is reviewed, and the same study is performed. Alternate polynomial presentations are given and are shown to involve the same matrices and similar fast algorithms.Keywords
This publication has 12 references indexed in Scilit:
- Linear statistical models for stationary sequences and related algorithms for Cholesky factorization of Toeplitz matricesIEEE Transactions on Acoustics, Speech, and Signal Processing, 1987
- A note on the evaluation of complex integrals using filtering interpretationsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1982
- Generation of cross-covariance sequencesIEEE Transactions on Acoustics, Speech, and Signal Processing, 1981
- Maximum entropy and the relationship of the partial autocorrelation to the reflection coefficients of a layered systemIEEE Transactions on Acoustics, Speech, and Signal Processing, 1980
- Generating covariance sequences and the calculation of quantization and rounding error variances in digital filtersIEEE Transactions on Acoustics, Speech, and Signal Processing, 1980
- Statistical design of autoregressive-moving average digital filtersIEEE Transactions on Acoustics, Speech, and Signal Processing, 1979
- The use of second-order information in the approximation of discreate-time linear systemsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1976
- The inner formulation for the total square integral (SUM)Proceedings of the IEEE, 1973
- A numerical method for the evaluation of complex integralsIEEE Transactions on Automatic Control, 1970
- Factorization of the Covariance Generating Function of a Pure Moving Average ProcessSIAM Journal on Numerical Analysis, 1969