"This book presents the first systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honoring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e., the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements."--BOOK JACKET.

Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.

Covering a period of about 25 years, during which time-frequency has undergone significant developments, this book is principally addressed to researchers and engineers interested in non-stationary signal analysis and processing. It is written by recognized experts in the field.

This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.

This contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research. New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Topics covered include: Signal analysis Quantum theory Modulation space theory Applications to the medical industry Wavelet transform theory Anti-Wick operators Landscapes of Time-Frequency Analysis: ATFA 2019 will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

The present volume gathers contributions to the conference Microlocal and Time-Frequency Analysis 2018 (MLTFA18), which was held at Torino University from the 2nd to the 6th of July 2018. The event was organized in honor of Professor Luigi Rodino on the occasion of his 70th birthday. The conference’s focus and the contents of the papers reflect Luigi’s various research interests in the course of his long and extremely prolific career at Torino University.

Over the last few decades wireless communications, especially Mobile Communication Technology, has evolved by leaps and bounds. The mobile communication industry has named the different major changes as generations namely 1G, 2G,..5G. We are presently looking at deployment of 5G technologies. The work for 6G has already started. This book is focused on the waveform design of 6G. It presents a discourse on a potential waveform for 6G namely Orthogonal Time Frequency Space (OTFS) modulation. OTFS has a distinct feature when compared to earlier generation waveforms such that information bearing signal is placed in the delay Doppler domain as opposed to the usual placement of such signals in the time-frequency domain. This unique feature of OTFS enables it to overcome several disadvantages of a very popular and highly successful waveform namely Orthogonal Frequency Division Multiplexing (OFDM). OTFS is known to be more resilient to frequency offset and Doppler which is one of the key drawbacks of OFDM. With this feature, OTFS, can support higher mobility as well as higher frequency bands of operation which is also one of the key requirements of the next generation wireless communication technologies. The implementation complexity of OTFS remains comparable to that of OFDM. It is found that OTFS provides significant SNR advantage, higher resilience, lower PAPR, lower out of band signal leakage and higher multi-user spectral efficiency than that of OFDM. This book addresses• Fundamental signal model of OTFS. • Receiver design for OTFS• Channel estimation in OTFS• Multiple Access through non-orthogonal multiple access (NOMA-OTFS) The contents of the books are primarily outcome of the research work done at the G. S. Sanyal School of Telecommunications, Indian Institute of Technology Kharagpur, Kharagpur, India. Orthogonal Time Frequency Space Modulation : A waveform for 6G is ideal for personnel the wireless communication industry as well as academic staff and master/research students in electrical engineering with a specialization in wireless communications.

This book focuses on the mathematical and physical foundations of remote sensing digital image processing and introduces key algorithms utilized in this area. The book fully introduces the basic mathematical and physical process of digital imaging, the basic theory and algorithm of pixel image processing, and the higher-order image processing algorithm and its application. This book skillfully and closely integrates theory, algorithms, and applications, making it simple for readers to understand and use. Researchers and students working in the fields of remote sensing, computer vision, geographic information science, electronic information, etc., can profit from this book. For their work and research in digital image processing, they can master the fundamentals of imaging and image processing techniques.

This work introduces a new method for analysing measured signals: nonlinear mode decomposition, or NMD. It justifies NMD mathematically, demonstrates it in several applications and explains in detail how to use it in practice. Scientists often need to be able to analyse time series data that include a complex combination of oscillatory modes of differing origin, usually contaminated by random fluctuations or noise. Furthermore, the basic oscillation frequencies of the modes may vary in time; for example, human blood flow manifests at least six characteristic frequencies, all of which wander in time. NMD allows us to separate these components from each other and from the noise, with immediate potential applications in diagnosis and prognosis. Mat Lab codes for rapid implementation are available from the author. NMD will most likely come to be used in a broad range of applications.

It is widely recognised that mainstream economics has failed to translate micro consistently into macro economics and to provide endogenous explanations for the continual changes in the economic system. Since the early 1980s, a growing number of economists have been trying to provide answers to these two key questions by applying an evolutionary approach. This new departure has yielded a rich literature with enormous variety, but the unifying principles connecting the various ideas and views presented are, as yet, not apparent. This 2005 volume brings together fifteen original articles from scholars - each of whom has made a significant contribution to the field - in their common effort to reconstruct economics as an evolutionary science. Using meso economics as an analytical entity to bridge micro and macro economics as well as static and dynamic realms, a unified economic theory emerges.