Editing Adaptive filter (section)

===Nonlinear Adaptive Filters===
The goal of nonlinear filters is to overcome limitation of linear models. There are some commonly used approaches: Volterra LMS, [[Kernel adaptive filter]], Spline Adaptive Filter <ref>{{cite book|author1=Danilo Comminiello |author2= José C. Príncipe |title= Adaptive Learning Methods for Nonlinear System Modeling |date= 2018 |publisher=Elsevier Inc. |isbn= 978-0-12-812976-0}}</ref> and Urysohn Adaptive Filter.<ref>M.Poluektov and A.Polar. [http://ezcodesample.com/UAF/UAF.html Urysohn Adaptive Filter]. 2019.</ref><ref>{{Cite web|url=http://ezcodesample.com/NAF/index.html|title=Nonlinear Adaptive Filtering|website=ezcodesample.com}}</ref> Many authors <ref name=Liu2010>{{cite book|author1=Weifeng Liu |author2=José C. Principe |author3=Simon Haykin |title=Kernel Adaptive Filtering: A Comprehensive Introduction|date=March 2010|publisher=Wiley|isbn=978-0-470-44753-6|pages=12–20|url=http://media.wiley.com/product_data/excerpt/32/04704475/0470447532.pdf}}</ref> include also Neural networks into this list. The general idea behind Volterra LMS and Kernel LMS is to replace data samples by different nonlinear algebraic expressions. For Volterra LMS this expression is [[Volterra series]]. In Spline Adaptive Filter the model is a cascade of linear dynamic block and static non-linearity, which is approximated by splines.
In Urysohn Adaptive Filter the linear terms in a model

:<math> y_i= \sum_{j=0}^m w_{j} \ x_{ij} </math> 

are replaced by piecewise linear functions

:<math> y_i= \sum_{j=0}^m f_{j} ( x_{ij}) </math> 

which are identified from data samples.