This book is intended as a manual on modern advanced statistical methods for signal processing. The objectives of signal processing are the analysis, synthesis, and modification of signals measured from different natural phenomena, including engineering applications as well. Often the measured signals are affected by noise, distortion and incompleteness, and this makes it difficult to extract significant signal information. The main topic of the book is the extraction of significant information from measured data, with the aim of reducing the data size while keeping the basic information/knowledge about the peculiarities and properties of the analyzed system; to this aim, advanced and recently developed methods in signal analysis and treatment are introduced and described in depth. More in details, the book covers the following new advanced topics (and the corresponding algorithms), including detailed descriptions and discussions: the Eigen-Coordinates (ECs) method, The statistics of the fractional moments, The quantitative "universal" label (QUL) and the universal distribution function for the relative fluctuations (UDFRF), the generalized Prony spectrum, the Non-orthogonal Amplitude Frequency Analysis of the Smoothed Signals (NAFASS), the discrete geometrical invariants (DGI) serving as the common platform for quantitative comparison of different random functions. Although advanced topics are discussed in signal analysis, each subject is introduced gradually, with the use of only the necessary mathematics, and avoiding unnecessary abstractions. Each chapter presents testing and verification examples on real data for each proposed method. In comparison with other books, here it is adopted a more practical approach with numerous real case studies.

Auteur

Raoul Rashid Nigmatullin was born 24.09. in 1947 year in Tatar family in the town Kazan, which is being now the capital of Tatarstan Republic located inside the Russian Federation. He was born in the family of the young teacher Rashid Nigmatullin who later became the professor of radioelectronics and electrochemistry and rector of Kazan Aviation Institute. He obtained his intermediate education in Kazan in 1965 year, finishing the specialized school number 131 on physics and mathematics with silver medal. In 1970 year, he finished the physical faculty of Kazan State University with honors and received his Master Degree on specialization of theoretical physics. During 1970-1973 years, he was postgraduate student of the Theoretical Physics Department of Kazan University. From 1974 year he defended successfully his Candidate Thesis (which is equivalent to PhD thesis) and begun to work as an assistant on the department of Theoretical Physics. His PhD thesis was devoted to consideration of kinetics of paramagnets at low temperatures. From 1978 year he worked as a senior lecturer (Associate Professor) in the same department. He recommended himself as a good lecturer and read all traditional subjects of the theoretical physics: theoretical and quantum mechanics, thermodynamics and statistical physics and etc.).

In 1981 year, he participated in competition for the visiting as a probationer to the Great Britain. During of 1982 (September) -1983 (July) he worked as a scientific (postdoctoral) assistant in the laboratory of physics of dielectrics (former Chelsea-college of London University) under the leadership of Prof. A.K. Jonscher who was the well-known specialist in physics of dielectrics. Then in 1990 year, he was invited again for three month in the King's college (London University) to continue his investigations in dielectric relaxation phenomena in laboratory of Prof. Robert M.Hill. During November 1991-January 1992, he was invited by Dr. Alain Le Mehaute (ALCATEL ALSTHOM RESHERCHE, later ISMANS) in France to work in the region of fractal physics. In 1992 year, he defended successfully his doctorate thesis and obtained the full Doctorate degree of Physics and Mathematics. Beginning from the March 1994 year, he obtained the status of Full Professor in the Department of Theoretical Physics of Kazan State University. The High Attestation Committee from Moscow confirmed officially by the Professor's Diploma his Full Doctorate and Professor Status in 1997 year.

In November of 1993, he was invited by Prof. F. Mainardi to read lectures in Italy to Bologna University devoted to the mathematical physics of fractional calculus. This direction in physics is quite new one and establishes the new relationship between fractal physics and fractional calculus.

Starting from 2015 year, he is working as a contracting professor in Kazan National Research Technical University (KNRTU-KAI). His scientific publications are well known among the specialists working in dielectrics and physics of fractals not only in ex-Soviet Union but in the West as well. He collaborates actively with the scientists of many countries - Great Britain, France, Israel, Turkey, Japan,Italy and PRC.

Under his direct supervision 7 postgraduate students in Kazan Federal University have defended successfully their PhD thesis and one of them Dr. V. Toboev received the degree of Doctor of biophysics.

The American Biographical Institute selected his biography in annual books "The Contemporary Who's Who" (Who's Making a Difference) 2002/2003, 2007/2008 and 2010/2011 years. In 2012 year in the conference Nonlinear Science and Complexity (August, Budapest) he received the G. M. Zaslavsky European award for the solution of the Prony problem.

Now he has more than 250 publications in the different journals entering in the SCOPUS and WoS databases and is well-cited scientist among other leading Russian scientists actively working in the modern science. In accordance with the ISI (International Scientific Institute) version his total citation index CItot close to 3000 and the Hirsch index equalled 28. Each year he receives many invitations for visiting of many international universities for reading lectures related with his personal research. He visited Japan (2007), Turkey (2008/2009), PRC (Guangzhou 2010/2012), Norway (2013). In the 2014 year he read lectures in Shandong university (Jinan city, PRC). In the recent conferences "New Trends in Science and Technology" and "Fractional Derivatives and their Applications" (November 2008, Ankara, Turkey) and in the 4-th conference of "Nonlinear Science and Complexity" (August 2012, Hungary Budapest) he received some awards for his contribution in the development of new methods in signal/noise analysis and the methods of fractional calculus for analysis of different compl...

Contenu

In what cases the non-linear fitting problem is reduced to the well-known linear least square method? The Eigen-Coordinates method..- A nontrivial example of the application of the ECs method: Description of the blow-like signals..- The statistics of the fractional moments and its application for quantitative "reading" of real data..- The quantitative "universal" label (QUL) and the universal distribution function for the relative fluctuations (UDFRF). .- Description of the partly correlated random sequences: Replacement of the random sequences by the generalized Prony spectrum..- The general theory of reproducible and quasi-reproducible experiments..- Non-orthogonal Amplitude Frequency Analysis of the Smoothed Signals (NAFASS) and its application for the description of multi-frequency signals..- NIMRAD in action: Application