Sliding window adaptive fast QR and QR-lattice algorithms

Author

Baykal, Buyurman ; Constantinides, Anthony G.

Author_Institution

Dept. of Electr. & Electron. Eng., Baskent Univ., Ankara, Turkey

Volume

46

Issue

11

fYear

1998

fDate

11/1/1998 12:00:00 AM

Firstpage

2877

Lastpage

2887

Abstract

Sliding window formulations of the fast QR and fast QR-lattice algorithms are presented. The derivations are based on the partial triangularization of raw data matrices. Three methods for window downdating are discussed: the method of plane hyperbolic rotations, the Chambers´ method, and the LINPACK algorithm. A numerically ill-conditioned stationary signal and a speech signal are used in finite wordlength simulations of the full QR (nonfast), fast QR, and QR-lattice algorithms. All algorithms are observed to be numerically stable over billions of iterations for double-precision mantissas (53 bits), but as the number of bits is decreased in the mantissa, the algorithms exhibit divergent behavior. Hence, practically, the algorithms can de regarded as numerically stable for long wordlengths

Keywords

adaptive filters; adaptive signal processing; filtering theory; least squares approximations; matrix algebra; numerical stability; Chambers´ method; LINPACK algorithm; adaptive fast QR algorithm; adaptive fast QR-lattice algorithm; adaptive filters; data matrices; divergent behavior; double-precision mantissas; finite wordlength simulations; full QR nonfast algorithm; ill-conditioned stationary signal; iterations; least squares estimation; partial triangularization; plane hyperbolic rotations; sliding window algorithm; speech signal; stable algorithms; window downdating; Adaptive filters; Convergence; Covariance matrix; Equations; Matrix decomposition; Signal processing algorithms; Speech; Stability; Time varying systems;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.726802

Filename

726802