Chaos: Statistical Description and Nonlinear Filtering

This small book mainly is not dedicated to the people who can consider themselves as "pure" scientists and therefore are not interested in practical applications (beside they can also find in this book some interesting topics for research). The authors expect that their results might be useful for people whose interests lies in the area of real time applications, mainly in signal processing and communication fields, but not limited to them. First part of the book is completely dedicated to some basics of chaos considering it as a stochastic process and to the statistical description of chaos by means of cumulants and cumulant functions. The latter is not "traditional" in the common literature. The rest of the material is devoted to different aspects of the nonlinear filtering algorithms of chaos in presence of additive noise (Gaussian and non-Gausian). Some aspects of the material of this part are strongly related to the nonliear filtering of "weak" chaos, i.e to the scenarios, when the signal/noise ratio is less (or much less) than one. Such kind of scenarios can take place in bioelectronics, voice processing, etc.