A First Course In Fourier Analysis PDF Download
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Author | : David W. Kammler |
Publisher | : Cambridge University Press |
Total Pages | : 39 |
Release | : 2008-01-17 |
Genre | : Mathematics |
ISBN | : 1139469037 |
Download A First Course in Fourier Analysis Book in PDF, ePub and Kindle
This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.
Author | : Albert Boggess |
Publisher | : John Wiley & Sons |
Total Pages | : 248 |
Release | : 2011-09-20 |
Genre | : Mathematics |
ISBN | : 1118211154 |
Download A First Course in Wavelets with Fourier Analysis Book in PDF, ePub and Kindle
A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
Author | : Anton Deitmar |
Publisher | : Springer Science & Business Media |
Total Pages | : 154 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 147573834X |
Download A First Course in Harmonic Analysis Book in PDF, ePub and Kindle
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
Author | : Albert Boggess |
Publisher | : John Wiley & Sons |
Total Pages | : 336 |
Release | : 2015-08-21 |
Genre | : Mathematics |
ISBN | : 1119214327 |
Download A First Course in Wavelets with Fourier Analysis Book in PDF, ePub and Kindle
A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
Author | : Jose Garcia-Cuerva |
Publisher | : CRC Press |
Total Pages | : 336 |
Release | : 2018-01-18 |
Genre | : Mathematics |
ISBN | : 135108058X |
Download Fourier Analysis and Partial Differential Equations Book in PDF, ePub and Kindle
Contains easy access to four actual and active areas of research in Fourier Analysis and PDE Covers a wide spectrum of topics in present research Provides a complete picture of state-of-the-art methods in the field Contains 200 tables allowing the reader speedy access to precise data
Author | : Anders Vretblad |
Publisher | : Springer Science & Business Media |
Total Pages | : 275 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 0387217231 |
Download Fourier Analysis and Its Applications Book in PDF, ePub and Kindle
A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.
Author | : Robert T. Seeley |
Publisher | : Courier Corporation |
Total Pages | : 116 |
Release | : 2014-02-20 |
Genre | : Mathematics |
ISBN | : 0486151794 |
Download An Introduction to Fourier Series and Integrals Book in PDF, ePub and Kindle
A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers. Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to apply these results and methods to new situations. The chapter on Fourier transforms derives analogs of the results obtained for Fourier series, which the author applies to the analysis of a problem of heat conduction. Numerous computational and theoretical problems appear throughout the text.
Author | : Bao Luong |
Publisher | : Springer Science & Business Media |
Total Pages | : 167 |
Release | : 2009-08-14 |
Genre | : Mathematics |
ISBN | : 0817649166 |
Download Fourier Analysis on Finite Abelian Groups Book in PDF, ePub and Kindle
This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.
Author | : John B. Conway |
Publisher | : Cambridge University Press |
Total Pages | : 357 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 1107173140 |
Download A First Course in Analysis Book in PDF, ePub and Kindle
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.
Author | : Dinakar Ramakrishnan |
Publisher | : Springer Science & Business Media |
Total Pages | : 372 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475730853 |
Download Fourier Analysis on Number Fields Book in PDF, ePub and Kindle
A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.