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A streamlined theory is presented for adaptive filters within which the major adaptive filter algorithms can be seen as special cases. The algorithm development part of the theory involves three ingredients: a preconditioned Wiener Hopf equation, its simplest possible iterative solution through the Richardson iteration, and an estimation strategy for the autocorrelation matrix, the cross-correlation vector and a preconditioning matrix. This results in a generalised adaptive filter in which intuitively plausible parameter selections give the major adaptive filter algorithms as special cases. This provides a setting where the similarities and differences between the many different adaptive filter algorithms are clearly and explicitly exposed. Based on the authors' generalised adaptive filter, expressions for the learning curve, the excess mean square error and the mean square coefficient deviation are developed. These are general performance results that are directly applicable to the major families of adaptive filter algorithms through the selection of a few parameters. Finally, the authors demonstrate through simulations that these results are useful in predicting adaptive filter performance.
References
-
-
1)
-
T.K. Moon ,
W.C. Stirling
.
(2000)
Mathematical methods and algorithms for signal processing.
-
2)
-
H.-C. Shin ,
W.-J. Song ,
A.H. Sayed
.
Mean-square performance of data-reusing adaptive algorithm.
IEEE Signal Process. Lett.
,
12 ,
851 -
854
-
3)
-
H. Malvar
.
(1992)
Signal processing with lapped transforms.
-
4)
-
K.A. Lee ,
W.S. Gan
.
Improving convergence of the NLMS algorithm using constrained subband updates.
IEEE Signal Process. Lett.
,
9 ,
736 -
739
-
5)
-
J.H. Husøy
.
A preconditioned LMS adaptive filter.
ECTI Trans. Electr. Eng. Electron. Commun.
,
3 -
9
-
6)
-
Husøy, J.H., Abadi, M.S.E.: `A novel LMS-type adaptive filter optimized for operation in multiple signal environments', Proc. NORSIG, Stavanger, September 2005, Norway, p. 117–120.
-
7)
-
Husøy, J.H., Abadi, M.S.E.: `A new LMS-type algorithm utilizing approximate a priori knowledge of the input autocorrelation', Proc. Applied Electronics, September 2005, Plzen, Czech Republic, p. 147–150.
-
8)
-
Y. Saad
.
(1996)
Iterative methods for sparse linear systems.
-
9)
-
Husøy, J.H.: `A circulantly preconditioned NLMS-type adaptive filter', Proc. 17th Int. Conf. Radioelektronika, 2007, Brno, Czech Republic, p. 141–145.
-
10)
-
A.H. Sayed
.
(2003)
Fundamentals of adaptive filtering.
-
11)
-
J. Apolinario ,
M.L. Campos ,
P.S.R. Diniz
.
Convergence analysis of the binormalized data-reusing LMS algorithm.
IEEE Trans. Signal Process.
,
11 ,
3235 -
3242
-
12)
-
S.S. Pradhan ,
V.E. Reddy
.
A new approach to subband adaptive filtering.
IEEE Trans. Signal Process.
,
655 -
664
-
13)
-
L.F. Richardson
.
The approximate arithmetical solution by finite differences of physical problems involving differential equations with an application to the stresses to a masonry dam.
Philos. Trans. R. Soc. London, Ser. A
,
307 -
357
-
14)
-
N.R. Yousef ,
A.H. Sayed
.
A unified approach to the steady-state and tracking analysis of adaptive filters.
IEEE Trans. Signal Process.
,
314 -
324
-
15)
-
P.P. Vaidyanathan
.
(1993)
Multirate systems and filterbanks.
-
16)
-
P.S.R. Diniz
.
(2002)
Adaptive filtering: algorithms and practical implementation.
-
17)
-
T.Y. Al-Naffouri ,
A.H. Sayed
.
Transient analysis of data-normalized adaptive filters.
IEEE Trans. Signal Process.
,
3 ,
639 -
652
-
18)
-
K. Chen
.
(2005)
Matrix preconditioning techniques and applications.
-
19)
-
S. Haykin
.
(1996)
Adaptive filter theory.
-
20)
-
M. De Courville ,
P. Duhamel
.
Adaptive filtering in subbands using a weighted criterion.
IEEE Trans. Signal Process.
,
2359 -
2371
-
21)
-
H.-C. Shin ,
A.H. Sayed
.
Mean-square performance of a family of affine projection algorithms.
IEEE Trans. Signal Process.
,
1 ,
90 -
102
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