Adaptive Filtering - download pdf or read online

By L. Morales

ISBN-10: 9533071583

ISBN-13: 9789533071589

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Here, we only consider p  2 . Using (40) and Lemma 3, we can obtain the first-order and second-order partial derivatives of f e , e , expressed by   p2 1 f e   e    p  1  e f e, e  e    p  1  p  2  e 2 p4 (41a) e in real-valued cases, and     p p2 1 f e  e , e  e 2 p  2 p 4 2 .  1  f e e , e  e e 2 p  p  2  p4 2 f e, e e , e  e e 4   (41b) 29 Steady-State Performance Analyses of Adaptive Filters in complex-valued cases, respectively. 1 becomes  vp  2   b u 2  p  2  v , a u (44) and the steady-state performance for real LMP algorithms can be written as  EMSE   TEMSE  opt    u v2 p  2 a u vp  2   b u v  2 p2 .

The least mean squares (LMS) algorithm, which is the most popular adaptive filtering algorithm, has enjoyed enormous popularity due to its simplicity and robustness [2] [3]. Over the years several variants of LMS have been proposed to overcome some limitations of LMS algorithm by modifying the error estimation function from linearity to nonlinearity. Sign-error LMS algorithm is presented by its computational simplicity [4], least-mean fourth (LMF) algorithm is proposed for applications in which the plant noise has a probability density function with short tail [5], and the LMMN algorithm achieves a better steady state performance than the LMS algorithm and better stability properties than the LMF algorithm by adjusting its mixing parameter [6], [7].

2 Steady-State Performance Analyses of Adaptive Filters Bin Lin and Rongxi He College of Information Science and Technology, Dalian Maritime University, Dalian, China 1. Introduction Adaptive filters have become a vital part of many modern communication and control systems, which can be used in system identification, adaptive equalization, echo cancellation, beamforming, and so on [l]. The least mean squares (LMS) algorithm, which is the most popular adaptive filtering algorithm, has enjoyed enormous popularity due to its simplicity and robustness [2] [3].

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Adaptive Filtering by L. Morales

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