A well-understood special case of nonlinear signal processing is found in adaptive signal processing and control. In its classical setting, a parameterized linear system is used to represent a weakly nonlinear system around an operating point where the optimal parameterization is learnt from the observation of the system input and a desired system output using on-line parameter adaptation algorithms. This setting can be generalized to include parameterized nonlinear systems and to various learning architectures such as cascade system compensation in predistortion or equalization scenarios and parallel system compensation in echo cancellation.

The adaption algorithms need to be able to handle real-world problems with often limited information from the observed signals, as is the case for blind adaptation algorithms and other underdetermined signal processing problems such as singlechannel source separation. Furthermore, they need to achieve fast and accurate learning outcomes where the class of Recursive Prediction Error methods has recently been generalized to the nonlinear predistortion case. Finally, computational complexity and architecture often play a crucial role, e.g., when distributing
the learning algorithm over sensor networks where the sensor nodes may play the triple role of sensing/communicating physical data, of forming the substrate for nonlinear models based on reservoir computing, and of implementing the model adaptation algorithm.