A block floating-point treatment to the LMS algorithm: efficient realization and a roundoff error analysis

An efficient scheme is presented for implementing the LMS-based transversal adaptive filter in block floating-point (BFP) format, which permits processing of data over a wide dynamic range, at temporal and hardware complexities significantly less than that of a floating-point processor. Appropriate...

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Vydáno v:	IEEE Transactions on Signal Processing Ročník 53; číslo 12; s. 4536 - 4544
Hlavní autoři:	Mitra, A., Chakraborty, M., Sakai, H.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.12.2005 Institute of Electrical and Electronics Engineers (IEEE) Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Adaptive filters Algorithm design and analysis Algorithms Applied sciences Block floating-point arithmetic Blocking Convergence Detection, estimation, filtering, equalization, prediction Dynamic range Error analysis Errors Exact sciences and technology Filtering Floating point arithmetic Format Hardware Information theory Information, signal and communications theory least mean square methods Least squares approximation overflow Regression analysis Roundoff error Roundoff errors Signal and communications theory Signal, noise Studies Telecommunications and information theory Transversal filters Overflow(computer arithmetics) Filtering Error estimation least mean square methods Rounding error Processing time Data processing Adaptive filter Steady state Implementation Mean square error Quantization noise overflow Algorithm performance Block floating-point arithmetic roundoff errors Transverse filter Convergence rate Floating point Least mean squares methods
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	An efficient scheme is presented for implementing the LMS-based transversal adaptive filter in block floating-point (BFP) format, which permits processing of data over a wide dynamic range, at temporal and hardware complexities significantly less than that of a floating-point processor. Appropriate BFP formats for both the data and the filter coefficients are adopted, taking care so that they remain invariant to interblock transition and weight updating operation, respectively. Care is also taken to prevent overflow during filtering, as well as weight updating processes jointly, by using a dynamic scaling of the data and a slightly reduced range for the step size, with the latter having only marginal effect on convergence speed. Extensions of the proposed scheme to the sign-sign LMS and the signed regressor LMS algorithms are taken up next, in order to reduce the processing time further. Finally, a roundoff error analysis of the proposed scheme under finite precision is carried out. It is shown that in the steady state, the quantization noise component in the output mean-square error depends on the step size both linearly and inversely. An optimum step size that minimizes this error is also found out.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2005.859342