Tag: Fourier

Free Download An Introduction to Basic Fourier Series by Sergei K. Suslov
English | PDF | 2003 | 379 Pages | ISBN : 1402012217 | 25.6 MB
It was with the publication of Norbert Wiener’s book ”The Fourier In tegral and Certain of Its Applications" [165] in 1933 by Cambridge Univer sity Press that the mathematical community came to realize that there is an alternative approach to the study of c1assical Fourier Analysis, namely, through the theory of c1assical orthogonal polynomials. Little would he know at that time that this little idea of his would help usher in a new and exiting branch of c1assical analysis called q-Fourier Analysis. Attempts at finding q-analogs of Fourier and other related transforms were made by other authors, but it took the mathematical insight and instincts of none other then Richard Askey, the grand master of Special Functions and Orthogonal Polynomials, to see the natural connection between orthogonal polynomials and a systematic theory of q-Fourier Analysis. The paper that he wrote in 1993 with N. M. Atakishiyev and S. K Suslov, entitled "An Analog of the Fourier Transform for a q-Harmonic Oscillator" [13], was probably the first significant publication in this area. The Poisson k~rnel for the contin uous q-Hermite polynomials plays a role of the q-exponential function for the analog of the Fourier integral under considerationj see also [14] for an extension of the q-Fourier transform to the general case of Askey-Wilson polynomials. (Another important ingredient of the q-Fourier Analysis, that deserves thorough investigation, is the theory of q-Fourier series.

Free Download Frank Morgan, "Real Analysis and Applications: Including Fourier Series and the Calculus of Variations"
English | ISBN: 0821838415 | 2005 | 208 pages | PDF | 8 MB
Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury’s orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America’s national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory. The book is suitable for undergraduates interested in real analysis.

Free Download Representations of SU(2,1) in Fourier Term Modules by Roelof W. Bruggeman , Roberto J. Miatello
English | PDF EPUB (True) | 2023 | 217 Pages | ISBN : 303143191X | 30 MB
This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the "abelian" Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the "non-abelian" modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included.

Free Download Numerical Fourier Analysis, Second Edition by Gerlind Plonka , Daniel Potts , Gabriele Steidl , Manfred Tasche
English | PDF EPUB (True) | 2023 | 676 Pages | ISBN : 3031350049 | 80.2 MB
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis.

Free Download Fast Fourier Transform and Convolution Algorithms by Henri J. Nussbaumer
English | PDF | 1982 | 286 Pages | ISBN : 354011825X | 20.3 MB
In the first edition of this book, we covered in Chapter 6 and 7 the applications to multidimensional convolutions and DFT’s of the transforms which we have introduced, back in 1977, and called polynomial transforms. Since the publication of the first edition of this book, several important new developments concerning the polynomial transforms have taken place, and we have included, in this edition, a discussion of the relationship between DFT and convolution polynomial transform algorithms. This material is covered in Appendix A, along with a presentation of new convolution polynomial transform algorithms and with the application of polynomial transforms to the computation of multidimensional cosine transforms. We have found that the short convolution and polynomial product algorithms of Chap. 3 have been used extensively. This prompted us to include, in this edition, several new one-dimensional and two-dimensional polynomial product algorithms which are listed in Appendix B. Since our book is being used as part of several graduate-level courses taught at various universities, we have added, to this edition, a set of problems which cover Chaps. 2 to 8. Some of these problems serve also to illustrate some research work on DFT and convolution algorithms. I am indebted to Mrs A. Schlageter who prepared the manuscript of this second edition. Lausanne HENRI J. NUSSBAUMER April 1982 Preface to the First Edition This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms.

Free Download Differential Equations, Fourier Series, and Hilbert Spaces
by Raffaele Chiappinelli
English | 2023 | ISBN: 3111294854 | 220 pages | True PDF EPUB | 26.16 MB

Free Download D’oh! Fourier: Theory, Applications, And Derivatives (Primers In Electronics And Computer Science)

English | 2022 | ISBN: 1800611102 | 305 pages | True PDF | 27.91 MB
D’oh! Fourier introduces the Fourier transform and is aimed at undergraduates in Computer Science, Mathematics, and Applied Sciences, as well as for those wishing to extend their education. Formulated around ten key points, this accessible book is light-hearted and illustrative, with many applications. The basis and deployment of the Fourier transform are covered applying real-world examples throughout inductively rather than the theoretical approach deductively. The key components of the textbook are continuous signals analysis, discrete signals analysis, image processing, applications of Fourier analysis, together with the origin and nature of the transform itself. D’oh! Fourier is reproducible via MATLAB/Octave and is supported by a comprehensive website which provides the code contained within the book.

Free Download David Brandwood, "Fourier Transforms in Radar and Signal Processing (Artech House Radar Library Ed 2"
English | ISBN: 1608071979 | 2011 | 263 pages | PDF | 13 MB
Electrical engineers working in radar, sonar, and signal processing use Fourier transform relationships everyday on the job. This book presents a coordinated system for performing Fourier transforms on a variety of functions. It illustrates how to apply Fourier transforms to many specific examples in radar, signal processing, and antenna design.

Free Download Non-Fourier Heat Conduction: From Phase-Lag Models to Relativistic and Quantum Transport
English | 2023 | ISBN: 3031259726 | 773 Pages | PDF EPUB (True) | 18 MB
This book presents a broad and well-structured overview of various non-Fourier heat conduction models. The classical Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation becomes dominant and memory or non-local spatial effects become significant; e.g., during ultrafast heating, heat transfer at the nanoscale, in granular and porous materials, at extremely high values of the heat flux, or in heat transfer in biological tissues. The book looks at numerous non-Fourier heat conduction models that incorporate time non-locality for materials with memory, such as hereditary materials, including fractional hereditary materials, and/or spatial non-locality, i.e. materials with a non-homogeneous inner structure. Beginning with an introduction to classical transport theory, including phase-lag, phonon, and thermomass models, the book then looks at various aspects of relativistic and quantum transport, including approaches based on the Landauer formalism as well as the Green-Kubo theory of linear response. Featuring an appendix that provides an introduction to methods in fractional calculus, this book is a valuable resource for any researcher interested in theoretical and numerical aspects of complex, non-trivial heat conduction problems.

Published 5/2023
Created by Dr. Simen Li
MP4 | Video: h264, 1280×720 | Audio: AAC, 44.1 KHz, 2 Ch
Genre: eLearning | Language: English + srt | Duration: 30 Lectures ( 2h 15m ) | Size: 694 MB