Title :
Numerical behaviour of Toeplitz solutions
Author :
Papaodysseus, C. ; Koukoutsis, E. ; Carayanni, G.
Author_Institution :
Div. of Comput. Sci., Nat. Tech. Univ. of Athens, Greece
Abstract :
The numerical behavior of the order-recursive algorithms for the solution of a number of typical Toeplitz systems is studied. Use is made of a novel methodology that gives a direct interpretation of the positive definiteness that leads to the explicit computation of the minimum absolute bounds of the 1-step and l-step-ahead linear predictors. Ill-conditioning is discussed, and an algorithmic scheme with improved numerical behavior is given for the l-step-ahead LP case. It is proved that the Levinson algorithm, when it is used for the solution of the least-squares finite-impulse-response filtering problem, manifests a fundamentally different numerical behavior than when it is used for the l-step-ahead problem
Keywords :
filtering and prediction theory; Levinson algorithm; Toeplitz solutions; least-squares finite-impulse-response filtering; linear predictors; minimum absolute bounds; order-recursive algorithms; Autocorrelation; Computer science; Filtering; Finite impulse response filter; Heart; Lattices; Nonlinear filters; Speech;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1989. ICASSP-89., 1989 International Conference on
Conference_Location :
Glasgow
DOI :
10.1109/ICASSP.1989.266875
