By L. Morales
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Extra info for Adaptive Filtering
G. Larimore, and C. R. Hohnson, “Stationary and nonstationary learning characteristics of the LMS adaptive filter, ” Proc. 46, pp. 1151-1161, 1976.  V. J. Mathews and S. Cho, “Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm,” IEEE Trans. , Speech, Signal Processing, vol. 35, pp. 450-454, 1987.  E. Walah and B. Widrow, “The least-mean fourth (LMF) adaptive algorithm and its family,” IEEE Trans. Information Theory, vol. 30, pp. 275-283, 1984.  J.
5 In real-valued cases, f e , e 25 Steady-State Performance Analyses of Adaptive Filters where O ea , ea denotes third and higher-power terms of ea or ea . Ignoring O ea , ea 6, and taking expectations of both sides of the above equation, we get 1 1 E e , e E v , v E e v , v ea E e v , v ea . e. v , ea are mutually independent, and Eea Eea2 0 ), we obtain E e , e =E v , v E e , e v , v TEMSE 2 (21) where TEMSE is defined by (5).
5. 1. Fig. 6. 1 Steady-State Performance Analyses of Adaptive Filters Fig. 7. 1. Fig. 8. 1. 39 40 Adaptive Filtering Fig. 9. 2. Fig. 10. 1. Steady-State Performance Analyses of Adaptive Filters Fig. 11. 2. Fig. 12. Comparisons of the tracking performance between LMS algorithm and LMP algorithm in Gaussian noise environments and uniformly distributed noise environments. 41 42 Adaptive Filtering 5. Conclusions Based on the Taylor series expansion (TSE) and so-called complex Brandwood-form series expansion (BSE), this paper develops a unified approach for the steady-state mean-squareerror (MSE) and tracking performance analyses of adaptive filters.