Topics In Affine And Discrete Harmonic Analysis
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Topics In Affine And Discrete Harmonic Analysis
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Author : Jonathan Edward Hickman
language : en
Publisher:
Release Date : 2015
Topics In Affine And Discrete Harmonic Analysis written by Jonathan Edward Hickman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
Foundations Of Discrete Harmonic Analysis
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Author : Vasily N. Malozemov
language : en
Publisher: Springer Nature
Release Date : 2020-06-24
Foundations Of Discrete Harmonic Analysis written by Vasily N. Malozemov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-24 with Mathematics categories.
This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing. In a nutshell, DHA is used to determine the time-frequency structure of a digitized signal, providing a representation of the signal as a sum of spectral components that can then be analyzed. The main methods of DHA are discrete Fourier transform and other discrete orthogonal transforms such as the Walsh and Haar transforms. Fast algorithms are used to process signals in real time, while additional options are provided by spline harmonic analysis. These topics are carefully covered in the book. With only modest prerequisites, some of which are recalled at the beginning, a profound mathematical theory is built almost from scratch. The 150 exercises included form an integral part of the text. Based decades of teaching experience, this book provides a basis for lecture courses starting at the upper undergraduate level, and will also prove a valuable resource for mathematicians and engineers interested in digital signal processing.
The Xft Quadrature In Discrete Fourier Analysis
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Author : Rafael G. Campos
language : en
Publisher: Springer
Release Date : 2019-05-24
The Xft Quadrature In Discrete Fourier Analysis written by Rafael G. Campos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-24 with Mathematics categories.
This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.
Discrete Harmonic Analysis
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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-21
Discrete Harmonic Analysis written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-21 with Mathematics categories.
A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Harmonic Analysis
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Author : Palle E.T. Jorgensen
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-30
Harmonic Analysis written by Palle E.T. Jorgensen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-30 with Mathematics categories.
There is a recent and increasing interest in harmonic analysis of non-smooth geometries. Real-world examples where these types of geometry appear include large computer networks, relationships in datasets, and fractal structures such as those found in crystalline substances, light scattering, and other natural phenomena where dynamical systems are present. Notions of harmonic analysis focus on transforms and expansions and involve dual variables. In this book on smooth and non-smooth harmonic analysis, the notion of dual variables will be adapted to fractals. In addition to harmonic analysis via Fourier duality, the author also covers multiresolution wavelet approaches as well as a third tool, namely, L2 spaces derived from appropriate Gaussian processes. The book is based on a series of ten lectures delivered in June 2018 at a CBMS conference held at Iowa State University.
Advances In Discrete Tomography And Its Applications
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Author : Gabor T. Herman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-19
Advances In Discrete Tomography And Its Applications written by Gabor T. Herman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-19 with Technology & Engineering categories.
The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the book explores the various mathematical and computational problems of discrete tomography with an emphasis on new applications.
Harmonic Analysis
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-11-02
Harmonic Analysis written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-02 with Mathematics categories.
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 3 returns to the themes of Part 1 by discussing pointwise limits (going beyond the usual focus on the Hardy-Littlewood maximal function by including ergodic theorems and martingale convergence), harmonic functions and potential theory, frames and wavelets, spaces (including bounded mean oscillation (BMO)) and, in the final chapter, lots of inequalities, including Sobolev spaces, Calderon-Zygmund estimates, and hypercontractive semigroups.
A Course In Abstract Harmonic Analysis
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Author : Gerald B. Folland
language : en
Publisher: CRC Press
Release Date : 2016-02-03
A Course In Abstract Harmonic Analysis written by Gerald B. Folland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-03 with Mathematics categories.
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul
Advanced Topics In Mathematical Analysis
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Author : Michael Ruzhansky
language : en
Publisher: CRC Press
Release Date : 2019-01-08
Advanced Topics In Mathematical Analysis written by Michael Ruzhansky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.
Classical And Multilinear Harmonic Analysis
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Author : Camil Muscalu
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
Classical And Multilinear Harmonic Analysis written by Camil Muscalu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.