Download or read book Mastering the Discrete Fourier Transform in One Two or Several Dimensions written by Isaac Amidror and published by Springer Science & Business Media. This book was released on 2013-07-19 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.

Download or read book The DFT written by William L. Briggs and published by SIAM. This book was released on 1995-01-01 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.

Download or read book New Trends in Applied Harmonic Analysis written by Akram Aldroubi and published by Birkhäuser. This book was released on 2016-04-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.

Download or read book Essential Mathematics for NMR and MRI Spectroscopists written by Keith C Brown and published by Royal Society of Chemistry. This book was released on 2020-08-28 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a review of the important areas of mathematics, this book then covers many of the underlying theoretical and practical aspects of NMR and MRI spectroscopy from a maths point of view. Competence in algebra and introductory calculus is needed but all other maths concepts are covered. It will bridge a gap between high level and introductory titles used in NMR or MRI spectroscopy. Uniquely, it takes a very careful and pedagogical approach to the mathematics behind NMR and MRI. It leaves out very few steps, which distinguishes it from other books in the field. The author is an NMR laboratory manager and is sympathetic to the frustrations of trying to understand where some of the fundamental equations come from hence his desire to either explicitly derive all equations for the reader or direct them to derivations. This is an essential text aimed at graduate students who are beginning their careers in NMR or MRI spectroscopy and laboratory managers if they need an understanding of the theoretical foundations of the technique.

Download or read book Operator Related Function Theory and Time Frequency Analysis written by Karlheinz Gröchenig and published by Springer. This book was released on 2014-11-25 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.

Download or read book Bode s Law and the Discovery of Juno written by Clifford J. Cunningham and published by Springer. This book was released on 2017-06-02 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Johann Bode developed a so-called law of planetary distances best known as Bode’s Law. The story of the discovery of Juno in 1804 by Karl Harding tells how Juno fit into that scheme and is examined as it relates to the philosopher Georg Hegel’s 1801 thesis that there could be no planets between Mars and Jupiter. By 1804 that gap was not only filled but had three residents: Ceres, Pallas and Juno! When Juno was discovered no one could have imagined its study would call into question Newton’s law of gravity, or be the impetus for developing the mathematics of the fast Fourier transform by Carl Gauss. Clifford Cunningham, a dedicated scholar, opens to scrutiny this critical moment of astronomical discovery, continuing the story of asteroid begun in earlier volumes of this series. The fascinating issues raised by the discovery of Juno take us on an extraordinary journey. The revelation of the existence of this new class of celestial bodies transformed our understanding of the Solar System, the implications of which are thoroughly discussed in terms of Romantic Era science, philosophy, poetry, mathematics and astronomy. The account given here is based on both English and foreign correspondence and scientific papers, most of which are translated for the first time.

Download or read book Landscapes of Time Frequency Analysis written by Paolo Boggiatto and published by Springer. This book was released on 2019-01-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis 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 Mobile Networks for Biometric Data Analysis written by Massimo Conti and published by Springer. This book was released on 2016-07-27 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book showcases new and innovative approaches to biometric data capture and analysis, focusing especially on those that are characterized by non-intrusiveness, reliable prediction algorithms, and high user acceptance. It comprises the peer-reviewed papers from the international workshop on the subject that was held in Ancona, Italy, in October 2014 and featured sessions on ICT for health care, biometric data in automotive and home applications, embedded systems for biometric data analysis, biometric data analysis: EMG and ECG, and ICT for gait analysis. The background to the book is the challenge posed by the prevention and treatment of common, widespread chronic diseases in modern, aging societies. Capture of biometric data is a cornerstone for any analysis and treatment strategy. The latest advances in sensor technology allow accurate data measurement in a non-intrusive way, and in many cases it is necessary to provide online monitoring and real-time data capturing to support a patient’s prevention plans or to allow medical professionals to access the patient’s current status. This book will be of value to all with an interest in this expanding field.

Download or read book The Discrete Fourier Transform written by D. Sundararajan and published by World Scientific. This book was released on 2001 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and WalshOCoHadamard transforms. The large number of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book will be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. Errata(s). Preface, Page viii. OC www.wspc.com/others/software/4610/OCO. The above links should be replaced with. OC www.worldscientific.com/doi/suppl/10.1142/4610/suppl_file/4610_software_free.zipOCO. Contents: The Discrete Sinusoid; The Discrete Fourier Transform; Properties of the DFT; Fundamentals of the PM DFT Algorithms; The u X 1 PM DFT Algorithms; The 2 X 2 PM DFT Algorithms; DFT Algorithms for Real Data OCo I; DFT Algorithms for Real Data OCo II; Two-Dimensional Discrete Fourier Transform; Aliasing and Other Effects; The Continuous-Time Fourier Series; The Continuous-Time Fourier Transform; Convolution and Correlation; Discrete Cosine Transform; Discrete WalshOCoHadamard Transform. Readership: Upper level undergraduate students, graduates, researchers and lecturers in engineering and applied mathematics."

Download or read book Mathematics of Multidimensional Fourier Transform Algorithms written by Richard Tolimieri and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing algorithms for multi-dimensional Fourier transforms, this book presents results that yield highly efficient code on a variety of vector and parallel computers. By emphasising the unified basis for the many approaches to both one-dimensional and multidimensional Fourier transforms, this book not only clarifies the fundamental similarities, but also shows how to exploit the differences in optimising implementations. It will thus be of great interest not only to applied mathematicians and computer scientists, but also to seismologists, high-energy physicists, crystallographers, and electrical engineers working on signal and image processing.

Download or read book Fast Fourier Transform and Convolution Algorithms written by Henri J. Nussbaumer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Lectures on the Fourier Transform and Its Applications written by Brad G. Osgood and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques—all of which are important in many areas of engineering and science—the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.

Download or read book Discrete and Continuous Fourier Transforms written by Eleanor Chu and published by CRC Press. This book was released on 2008-03-19 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long employed in electrical engineering, the discrete Fourier transform (DFT) is now applied in a range of fields through the use of digital computers and fast Fourier transform (FFT) algorithms. But to correctly interpret DFT results, it is essential to understand the core and tools of Fourier analysis. Discrete and Continuous Fourier Transform

Download or read book NASA Tech Briefs written by and published by . This book was released on 1991 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discrete Fourier Transforms and their Applications written by Vaclav Cizek and published by CRC Press. This book was released on 1986-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed to be a practial handbook on the evaluation and application of one of the major techniques for discrete signal processing. Knowledge of the discrete Fourier transform (DFT) and the ability to construct alogorithms based on the techniques of fast Fourier analysis are essential prerequisites for communications and cybernetics engineers. These methods are also of inestimable value to applied scientists in many other fields. The treatment given here is aimed specifically at such experimentalists and practitioners, and includes only such mathematical development as is necessary to give a feel for the significance of the methods, and to promote proficiency in its use. An introductory discourse on the general theory of Fourier series and transforms is followed by a thorough review of the properties and means of computation of the DFT. The fast Fourier transform is presented as a particularly efficient algorithm for DFT evaluation, and is described in some detail. Some applications of DFT's are discussed, and the book is rounded off with an introduction to discrete Hilbert transforms. Examples are provided throughout the text, and a full bibliography provides the basis for further study of the mathematical theory and specific areas of application.

Download or read book Simpson s Discrete Fourier Transform written by Dan Sibandze and published by LAP Lambert Academic Publishing. This book was released on 2015-02-27 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text we derive the Simpson Discrete Fourier Transform (SDFT) by applying numerical quadrature to approximate Fourier coefficents of periodic functions. This a an alternative transformation to the Classical Discrete Fourier Transform (DFT). A purely mathematical approach is taken to derive several properties including time reversal, even time shift, frequency shift, convolution, duality and Plancherel's theorem. Using the duality property recursively a detailed analysis of the discrete spectrum is provided. A two dimensional transform is subsequently derived and applied to encryption and watermarking in the frequency domain. The amplitude spectrum is distinctively different from that of the DFT due to the appearance of extra bright regions. Here the emphasis is on the mathematics and structure of the transform with the applications being coincidental. We envisage that this transform will find many applications in several engineering fields.

Download or read book Fast Fourier Transforms Second Edition written by James S. Walker and published by CRC Press. This book was released on 1996-08-22 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :