4. Introduction to adaptive filtering

4.1 Different algorithms

An adaptive filter is a digital filter whose coefficients change according to the signals received. These coefficients will be estimated by recursive algorithms, in the sense of a certain criterion.

The criteria generally used to obtain these algorithms are of the least-squares type, as they lead to the simplest results to interpret. The filters can be finite impulse response (FIR) or infinite impulse response (IIR), and the structure can be either transverse or lattice.

The resulting families of algorithms have different arithmetic complexities, and their behavior depends on the type of excitation and the presence or absence of noise.

We will consider two main families of algorithms, based...