Title :
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
fDate :
11/1/1998 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
