Adaptive Filtering by L. Morales

By L. Morales

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R. Yousef and A. H. Sayed, “Fixed-point steady-state analysis of adaptive filters,” Int. J. Contr. Signal Processing, vol. 17, pp. 237-258, 2003. [19] B. Lin, R. He, X. Wang and B. Wang, “The excess mean square error analyses for Bussgang algorithm,” IEEE Signal Processing Letters, vol. 15, pp. 793-796, 2008. [20] A. Goupil and J. Palicot, “A geometrical derivation of the excess mean square error for Bussgang algorithms in a noiseless environment”, ELSEVIER Signal Processing, vol. 84, pp. 311-315, May, 2004.

Widrow, “The least-mean fourth (LMF) adaptive algorithm and its family,” IEEE Trans. Information Theory, vol. 30, pp. 275-283, 1984. [6] J. A. Chambers, O. Tanrikulu and A. G. Constantinides, “Least mean mixed-norm adaptive filtering,” Electron. , vol. 30, pp. 1574-1575, 1994. [7] O. Tanrikulu and J. A. Chambers, “Convergence and steady-state properties of the leastmean mixed-norm (LMMN) adaptive algorithm,” IEE Proceedings- Vision, Image Signal Processing, vol. 143, pp137-142, 1996. [8] B. Lin, R.

This assumption is referred to as the separation principle in [11]. 4, and using (4), we can rewrite (10) as      uE e , e   uEq e , e   1Tr  Q  (11) where  u  E  u   u  Eg  u  , 2 2 g u     .   q  e, e   f  e, e   Lemma 1 If e is complex-valued, and   e , e  and q  e , e  are defined by (12), then  e , e  2 Re  ea f e , e  ,     2  1  f e  v , v   2     2    e , e v , v  2 Re f e 1 v , v ,  v , v  0,   (12) 4    2 1 q e , e v , v  f e  v , v  2  2 Re  f  v , v f e, e v , v     2 .

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