New Digital Signal Processing Methods, 1st ed. 2020 Applications to Measurement and Diagnostics

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.

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

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 considerationof 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(A