Adaptive filter theory
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the selection of optimal nonlinearities for stochastic gradient adaptive algorithms
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
A nonlinear analytical model for the quantized LMS algorithm-thearbitrary step size case
IEEE Transactions on Signal Processing
A time-domain feedback analysis of filtered-error adaptive gradientalgorithms
IEEE Transactions on Signal Processing
A feedback approach to the steady-state performance of fractionallyspaced blind adaptive equalizers
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A unified approach to the steady-state and tracking analyses ofadaptive filters
IEEE Transactions on Signal Processing
H∞ optimality of the LMS algorithm
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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This paper develops a unified approach to the analysis and design of adaptive filters with error nonlinearities. In particular, the paper performs stability and steady-state analysis of this class of filters under weaker conditions than what is usually encountered in the literature, and without imposing any restriction on the color or statistics of the input. The analysis results are subsequently used to derive an expression for the optimum nonlinearity, which turns out to be a function of the probability density function of the estimation error. Some common nonlinearities are shown to be approximations to the optimum nonlinearity. The framework pursued here is based on energy conservation arguments.