4.6 Introduction to adaptive filters

In many applications requiring filtering, the necessary frequency response may not be known beforehand, or it may vary withtime. (Example; suppression of engine harmonics in a car stereo.) In such applications, an adaptive filter which can automaticallydesign itself and which can track system variations in time is extremely useful. Adaptive filters are used extensively in a widevariety of applications, particularly in telecommunications.

Outline of adaptive filter material

• Wiener filters

  $L_2$ optimal (FIR) filter design in a statistical context

• Lms algorithm

  simplest and by-far-the-most-commonly-used adaptive filter algorithm

• Stability and performance of the lms algorithm

  When and how well it works

• Applications of adaptive filters

  Overview of important applications

• Introduction to advanced adaptive filter algorithms

  Techniques for special situations or faster convergence