Tag: Fourier

Free Download Ronald Bracewell, "Fourier Analysis and Imaging"
English | 2003 | pages: 703 | ISBN: 0306481871, 1461347386 | DJVU | 11,2 mb
As Lord Kelvin said, "Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics." This has remained durable knowledge for a century, and has extended its applicability to topics as diverse as medical imaging (CT scanning), the presentation of images on screens and their digital transmission, remote sensing, geophysical exploration, and many branches of engineering. Fourier Analysis and Imaging is based on years of teaching a course on the Fourier Transform at the senior or early graduate level, as well as on Prof. Bracewell’s 1995 text Two-Dimensional Imaging. It is an excellent textbook and will also be a welcome addition to the reference library of those many professionals whose daily activities involve Fourier analysis in its many guises.

Free Download Fourier Modal Method and Its Applications in Computational Nanophotonics By Hwi Kim, Junghyun Park, Byoungho Lee
2012 | 326 Pages | ISBN: 1420088386 | PDF | 15 MB
Most available books on computational electrodynamics are focused on FDTD, FEM, or other specific technique developed in microwave engineering. In contrast, Fourier Modal Method and Its Applications in Computational Nanophotonics is a complete guide to the principles and detailed mathematics of the up-to-date Fourier modal method of optical analysis. It takes readers through the implementation of MATLAB® codes for practical modeling of well-known and promising nanophotonic structures. The authors also address the limitations of the Fourier modal method.Features Provides a comprehensive guide to the principles, methods, and mathematics of the Fourier modal method Explores the emerging field of computational nanophotonics Presents clear, step-by-step, practical explanations on how to use the Fourier modal method for photonics and nanophotonics applications Includes the necessary MATLAB codes, enabling readers to construct their own code Using this book, graduate students and researchers can learn about nanophotonics simulations through a comprehensive treatment of the mathematics underlying the Fourier modal method and examples of practical problems solved with MATLAB codes.

Free Download Sujaul Chowdhury, "Numerical Exploration of Fourier Transform and Fourier Series: The Power Spectrum of Driven Damped Oscillators "
English | ISBN: 3031346637 | 2024 | 116 pages | PDF | 1382 KB
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by Descriptionting velocity versus displacement rather than displaying displacement as a function of time. This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform.

Free Download Fourier Analysis on Polytopes and the Geometry of Numbers
by Robins, Sinai;
English | 2024 | ISBN: 1470470330 | 352 pages | True PDF | 33.76 MB

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