A roundoff error analysis of the LMS adaptive algorithm
- 1 February 1984
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Acoustics, Speech, and Signal Processing
- Vol. 32 (1) , 34-41
- https://doi.org/10.1109/tassp.1984.1164286
Abstract
The steady state output error of the least mean square (LMS) adaptive algorithm due to the finite precision arithmetic of a digital processor is analyzed. It is found to consist of three terms: 1) the error due to the input data quantization, 2) the error due to the rounding of the arithmetic operations in calculating the filter's output, and 3) the error due to the deviation of the filter's coefficients from the values they take when infinite precision arithmetic is used. The last term is of paricular interest because its mean squared value is inversely proportional to the adaptation step size μ. Both fixed and floating point arithmetics are examined and the expressions for the final mean square error are found to be similar. The relation between the quantization error and the error that occurs when adaptation possibly ceases due to quantization is also investigated.Keywords
This publication has 10 references indexed in Scilit:
- A continuously-adaptive filter implemented as a lattice structurePublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- Finite word length arithmetic computational error effects on the LMS adaptive weightsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2005
- On the advantages of the LMS spectrum analyzer over nonadaptive implementations of the sliding-DFTIEEE Transactions on Circuits and Systems I: Regular Papers, 1995
- Convergence analysis of LMS filters with uncorrelated Gaussian dataIEEE Transactions on Acoustics, Speech, and Signal Processing, 1985
- Recursive least squares ladder estimation algorithmsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1981
- On the Independence Theory of Equalizer ConvergenceBell System Technical Journal, 1979
- Quantization errors in floating-point arithmeticIEEE Transactions on Acoustics, Speech, and Signal Processing, 1978
- Stationary and nonstationary learning characteristics of the LMS adaptive filterProceedings of the IEEE, 1976
- On Local Roundoff Errors in Floating-Point ArithmeticJournal of the ACM, 1973
- On the design of gradient algorithms for digitally implemented adaptive filtersIEEE Transactions on Circuit Theory, 1973