Time-Frequency Analysis of Operators
Time-Frequency Analysis of Operators

Author: Elena Cordero

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-09-21

Total Pages: 458

ISBN-13: 311053245X

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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.

Foundations of Time-Frequency Analysis
Foundations of Time-Frequency Analysis

Author: Karlheinz Gröchenig

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 367

ISBN-13: 1461200032

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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.

Time-Frequency Analysis of Operators
Time-Frequency Analysis of Operators

Author: Elena Cordero

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-09-21

Total Pages: 340

ISBN-13: 3110530600

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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.

Time-frequency Analysis
Time-frequency Analysis

Author: Leon Cohen

Publisher: Prentice Hall

Published: 1995

Total Pages: 299

ISBN-13: 9780135945322

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Featuring traditional coverage as well as new research results that, until now, have been scattered throughout the professional literature, this book brings together—in simple language—the basic ideas and methods that have been developed to study natural and man-made signals whose frequency content changes with time—e.g., speech, sonar and radar, optical images, mechanical vibrations, acoustic signals, biological/biomedical and geophysical signals. Covers time analysis, frequency analysis, and scale analysis; time-bandwidth relations; instantaneous frequency; densities and local quantities; the short time Fourier Transform; time-frequency analysis; the Wigner representation; time-frequency representations; computation methods; the synthesis problem; spatial-spatial/frequency representations; time-scale representations; operators; general joint representations; stochastic signals; and higher order time-frequency distributions. Illustrates each concept with examples and shows how the methods have been extended to other variables, such as scale. For engineers, acoustic scientists, medical scientists and developers, mathematicians, physicists, and mangers working in the fields of acoustics, sonar, radar, image processing, biomedical devices, communication.

Time-Frequency Analysis
Time-Frequency Analysis

Author: Franz Hlawatsch

Publisher: John Wiley & Sons

Published: 2013-03-01

Total Pages: 377

ISBN-13: 1118623835

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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.

Discrete Fourier Analysis
Discrete Fourier Analysis

Author: M. W. Wong

Publisher: Springer Science & Business Media

Published: 2011-05-30

Total Pages: 175

ISBN-13: 3034801165

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This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.

Time‒Frequency and Time‒Scale Methods
Time‒Frequency and Time‒Scale Methods

Author: Jeffrey A. Hogan

Publisher: Springer Science & Business Media

Published: 2007-12-21

Total Pages: 403

ISBN-13: 0817644318

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Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.

Time-Frequency Signal Analysis and Processing
Time-Frequency Signal Analysis and Processing

Author: Boualem Boashash

Publisher: Academic Press

Published: 2015-12-11

Total Pages: 1070

ISBN-13: 0123985250

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Time-Frequency Signal Analysis and Processing (TFSAP) is a collection of theory, techniques and algorithms used for the analysis and processing of non-stationary signals, as found in a wide range of applications including telecommunications, radar, and biomedical engineering. This book gives the university researcher and R&D engineer insights into how to use TFSAP methods to develop and implement the engineering application systems they require. New to this edition: - New sections on Efficient and Fast Algorithms; a "Getting Started" chapter enabling readers to start using the algorithms on simulated and real examples with the TFSAP toolbox, compare the results with the ones presented in the book and then insert the algorithms in their own applications and adapt them as needed. - Two new chapters and twenty three new sections, including updated references. - New topics including: efficient algorithms for optimal TFDs (with source code), the enhanced spectrogram, time-frequency modelling, more mathematical foundations, the relationships between QTFDs and Wavelet Transforms, new advanced applications such as cognitive radio, watermarking, noise reduction in the time-frequency domain, algorithms for Time-Frequency Image Processing, and Time-Frequency applications in neuroscience (new chapter). - A comprehensive tutorial introduction to Time-Frequency Signal Analysis and Processing (TFSAP), accessible to anyone who has taken a first course in signals - Key advances in theory, methodology and algorithms, are concisely presented by some of the leading authorities on the respective topics - Applications written by leading researchers showing how to use TFSAP methods

Modulation Spaces
Modulation Spaces

Author: Árpád Bényi

Publisher: Springer Nature

Published: 2020-02-22

Total Pages: 177

ISBN-13: 1071603329

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This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.

Landscapes of Time-Frequency Analysis
Landscapes of Time-Frequency Analysis

Author: Paolo Boggiatto

Publisher: Springer

Published: 2019-01-30

Total Pages: 358

ISBN-13: 3030052109

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The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.