Abstract
Adaptive filtering is an important subfield of digital signal processing having been actively researched for more than four decades and having important applications such as noise cancellation, system identification, and telecommunications channel equalization. In this paper we provide a novel framework for adaptive filtering based on the theory stationary iterative linear equation solvers. We show that a large number of established, and some quite novel, adaptive filtering algorithms can be interpreted as special cases of a generic update equation forming the cornerstone of our framework. The novelty of our contribution is the casting of the adaptive filtering problem as a problem in numerical linear algebra facilitating a clearer understanding and a unified analysis of the various algorithms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Haykin, S.: Adaptive Filter Theory. Prentice Hall, Upper Saddle River (2002)
Treichler, J.R., Johnson, C.R., Larimore, M.G.: Theory and design of Adaptive filters. Prentice Hall, Upper Saddle River (2001)
Bose, T., Xu, G.F.: The Euclidian direction search algorithm in adaptive filtering. IEICE Trans. Fundamentals E85-A(3), 532–539 (2002)
Husøy, J.H.: RAMP: An adaptive filter with links to matching pursuits and iterative linear equation solvers. In: Proc. ISCAS, Bangkok, Thailand, May 2003, pp. IV–381–384 (2003)
Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing (1996)
Keller, H.B.: On the solution of singular and semidefinite linear systems by iteration. SIAM J. Numer. Anal. 2(2), 281–290 (1965)
Shin, H.-C., Sayed, A.H.: Transient behavior of affine projection algorithms. In: Proc. Int. Conf. Acoust. Speech, Signal Proc., Hong Kong, April 2003, pp. VI–353–356 (2003)
Husøy, J.H., Abadi, M.S.E.: Interpretation and convergence speed of two recently introduced adaptive filters (FEDS/RAMP) (2004) (Submitted)
Husøy, J.H., Abadi, M.S.E.: A common framework for transient analysis of adaptive filters. In: Proc. Melecon, Dubrovnik, Croatia, May 2004, pp. 265–268 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Husøy, J.H. (2005). Adaptive Filters Viewed as Iterative Linear Equation Solvers. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-31852-1_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24937-5
Online ISBN: 978-3-540-31852-1
eBook Packages: Computer ScienceComputer Science (R0)