A streamlined approach to adaptive filters

In this paper we present a streamlined framework for adaptive filters within which all major adaptive filter algorithms can be seen as special cases. The framework involves three ingredients: 1) A preconditioned Wiener Hopf Equation, 2) Its simplest possible iterative solution through the Richardson iteration, and 3) An estimation strategy for the autocorrelation matrix, the cross correlation vector and a preconditioning matrix. This results in a unified adaptive filter theory characterized by simplicity, elegance and economy of ideas suitable for an educational setting in which the similarities and differences between the many different adaptive filter algorithms are stressed.