Wavelets in identification wavelets, splines, neurons, fuzzies : how good for identification

This is a tutorial about nonparametric nonlinear system identification. Advantages and limitations of this approach are discussed from the engineer's point of view. Classical as well as modern techniques are discussed, this includes kernel and projection estimates, neural networks and hinging hyperplanes, and mainly wavelet estimators. Both practical and mathematical issues are investigated. Advantages and limitations of wavelet based techniques are emphazised. Finally we show how fuzzy models may play a role in this game, as a framework for expressing prior knowledge on the system. The whole material is illustrated on some application examples.