On the convergence of the CORDIC adaptive lattice filtering (CALF) algorithm

Author

Hu, Yu Hen

Author_Institution

Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA

Volume

46

Issue

7

fYear

1998

fDate

7/1/1998 12:00:00 AM

Firstpage

1861

Lastpage

1871

Abstract

In this paper, the convergence of a previously proposed CORDIC adaptive lattice filtering (CALF) algorithm is proved. It is shown that the update of the rotation angle (which is equivalent to the reflection coefficient) can be modeled by the state transition of a regular Markov chain, with each rotation angle being a state. The convergence of the CALF algorithm then is established as this Markov chain converges from an initial state probability distribution to its limiting state probability distribution. Formulae that enable explicit calculation of the limiting state distribution are derived. Moreover, it is shown that the algorithm has an exponential convergence rate

Keywords

Markov processes; adaptive filters; convergence of numerical methods; iterative methods; lattice filters; statistical analysis; CALF algorithm; CORDIC adaptive lattice filtering algorithm; exponential convergence rate; initial state probability distribution; limiting state probability distribution; reflection coefficient; regular Markov chain; rotation angle; state transition; update; Adaptive filters; Arithmetic; Convergence; Filtering algorithms; Iterative algorithms; Lattices; Probability distribution; Reflection; Signal processing algorithms; Stochastic processes;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.700954

Filename

700954