ABSTRACT
This chapter presents the celebrated least mean square (LMS) algorithm, developed by Widrow and Hoff in 1960. This algorithm is a member of stochastic gradient algorithms, and because of its robustness and low computational complexity, it has been used in a wide spectrum of applications. The chapter introduces the procedures of filtering random signals. An important consideration for the implementation of an adaptive filter is the requirement that the error signal be available to the adaptive algorithm. The adaptive filter is a two-coefficient filter. The noise is white and Gaussian distributed. It is recommended that the readers repeat the examples by varying all the different parameters, the noise amplitude, the signal amplitude, etc. so that it requires experience of the sensitivity of these factors to obtain a solution. The inverse of an unknown filter (system), the author place the adaptive filter in series with the unknown system.
