Download or read book Time Frequency Analysis of Some Generalized Fourier Transforms written by Mohammad Younus Bhat and published by BoD – Books on Demand. This book was released on 2023-09-13 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the world of physical science, important physical quantities like sound, pressure, electrical current, voltage, and electromagnetic fields vary with time. Such quantities are labeled as signals/waveforms and include oral signals, optical signals, acoustic signals, biomedical signals, radar, and sonar. Time-frequency analysis is a vital aid in signal analysis, which is concerned with how the frequency of a function (or signal) behaves in time, and it has evolved into a widely recognized applied discipline of signal processing. This book discusses the Fourier transform (FT), which is one of the most valuable and widely used integral transforms that converts a signal from time versus amplitude to frequency versus amplitude. It is one of the oldest tools in the time-frequency analysis of signals. The book includes five chapters that discuss general Fourier transforms as well as new and novel transforms such as hybrid transforms, quadratic-phase Fourier transforms, fractional Fourier transforms, linear canonical transforms, and more.
Download or read book Time Frequency Analysis of Operators written by Elena Cordero and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-09-21 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Time Frequency Analysis written by Karlheinz Gröchenig and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Time frequency Analysis written by Leon Cohen and published by Prentice Hall. This book was released on 1995 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applications of Fourier Transforms to Generalized Functions written by M. Rahman and published by WIT Press. This book was released on 2011 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized function is one of the important branches of mathematics which has enormous applications in practical fields. In particular its applications to the theory of distribution and signal processing are very much essential. In this computer age, information science plays a very important role and the Fourier transform is extremely significant in deciphering obscured information to be made understandable. The book contains six chapters and three appendices. Chapter 1 deals with the preliminary remarks of Fourier series from general point of view. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. Chapter 4 deals with the asymptotic estimation of Fourier transforms. Chapter 5 is devoted to the study of Fourier series as a series of generalized functions. Chapter 6 deals with the fast Fourier transforms.Appendix A contains the extended list of Fourier transform pairs.Appendix B illustrates the properties of impulse function.Appendix C contains an extended list of biographical references
Download or read book Time Frequency and Time Scale Methods written by Jeffrey A. Hogan and published by Springer Science & Business Media. This book was released on 2007-12-21 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Recent Developments in Time Frequency Analysis written by Leon Cohen and published by Springer Science & Business Media. This book was released on 1998-10-31 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Developments in Time-Frequency Analysis brings together in one place important contributions and up-to-date research results in this fast moving area. Recent Developments in Time-Frequency Analysis serves as an excellent reference, providing insight into some of the most challenging research issues in the field.
Download or read book Wavelet Transforms and Their Applications written by Lokenath Debnath and published by Springer. This book was released on 2014-11-25 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.
Download or read book Practical Time Frequency Analysis written by Rene Carmona and published by Academic Press. This book was released on 1998-08-27 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France. Detailed presentation of the Wavelet and Gabor transforms Applications to deterministic and random signal theory Spectral analysis of nonstationary signals and processes Numerous practical examples ranging from speech analysis to underwater acoustics, earthquake engineering, internet traffic, radar signal denoising, medical data interpretation, etc Accompanying software and data sets, freely downloadable from the book's Web page
Download or read book Data Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Download or read book Generalized Functions and Fourier Analysis written by Michael Oberguggenberger and published by Birkhäuser. This book was released on 2017-05-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.
Download or read book Time Frequency Analysis written by Azeemsha Thacham Poyil and published by LAP Lambert Academic Publishing. This book was released on 2012-06 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: The usual method for time-frequency representation using Short Time Fourier Transform or Spectrogram does not give precise time frequency information; hence the analysis of signal using them is not much easy. The Wigner Ville Distribution (WVD) can be used for a time-frequency representation of signals with a very good resolution in time and frequency domain. WVD has many features which make them suitable for applications in transient signal detection. This book talks about different time frequency signal representations including Wigner Ville Distribution and presents some methods to reduce the cross terms in WVD. The book also describes some important applications of the variants of WVD in the world of signal processing. This book will help a student or a researcher to learn about time frequency representations and to understand how to use them in a variety of applications.
Download or read book Signal Analysis written by Ronald L. Allen and published by John Wiley & Sons. This book was released on 2004-06-07 with total page 961 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
Download or read book Landscapes of Time Frequency Analysis written by Paolo Boggiatto and published by Springer Nature. This book was released on 2020-11-21 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Time Frequency Analysis written by Boualem Boashash and published by Elsevier. This book was released on 2003-10-16 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time Frequency Signal Analysis and Processing covers fundamental concepts, principles and techniques, treatment of specialised and advanced topics, methods and applications, including results of recent research. This book deals with the modern methodologies, key techniques and concepts that form the core of new technologies used in IT, multimedia, telecommunications as well as most fields of engineering, science and technology. It focuses on advanced techniques and methods that allow a refined extraction and processing of information, allowing efficient and effective decision making that would not be possible with classical techniques. The Author, fellow of IEEE for Pioneering contributions to time-frequency analysis and signal processing education, is an expert in the field, having written over 300 papers on the subject over a period pf 25 years. This is a REAL book, not a mere collection of specialised papers, making it essential reading for researchers and practitioners in the field of signal processing. *The most comprehensive text and reference book published on the subject, all the most up to date research on this subject in one place *Key computer procedures and code are provided to assist the reader with practical implementations and applications *This book brings together the main knowledge of time-frequency signal analysis and processing, (TFSAP), from theory and applications, in a user-friendly reference suitable for both experts and beginners
Download or read book The Analytical Theory of Heat written by Jean-Baptiste-Joseph Fourier and published by . This book was released on 1878 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
