Finite precision arithmetic and the Schur algorithm

Author

Zarowski, Christopher J. ; Card, Howard C.

Author_Institution

Dept. of Electr. Eng., Manitoba Univ., Winnipeg, Man., Canada

Volume

38

Issue

8

fYear

1990

fDate

8/1/1990 12:00:00 AM

Firstpage

1475

Lastpage

1478

Abstract

The numerical behavior of the Schur algorithm under fixed-point arithmetic conditions is investigated. It was found that the variance of the reflection coefficient estimates is large when the autocorrelation coefficients used to obtain the estimates are obtained from a narrowband low-pass signal. This is because such signals yield ill-conditioned autocorrelation matrices and is not due to numerical instability in the Schur algorithm. The effects of quantization errors tend to propagate through the later stages of the reflection coefficient computation in this instance. As a result, the Schur algorithm has numerical properties similar to those of the Durbin algorithm

Keywords

digital arithmetic; signal processing; Schur algorithm; autocorrelation coefficients; finite precision arithmetic; fixed-point arithmetic; ill-conditioned autocorrelation matrices; narrowband low-pass signal; quantization errors; reflection coefficient; variance; Algorithm design and analysis; Distribution functions; Filters; Fixed-point arithmetic; Image enhancement; Matrix decomposition; Random variables; Signal processing algorithms; Speech; Symmetric matrices;

fLanguage

English

Journal_Title

Acoustics, Speech and Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

0096-3518

Type

jour

DOI

10.1109/29.57588

Filename

57588