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Elsevier

Books in Fourier analysis

  • Optical Communications from a Fourier Perspective

    Fourier Theory and Optical Fiber Devices and Systems
    • 1st Edition
    • Palle Jeppesen + 1 more
    • English
    Optical Communications from a Fourier Perspective: Fourier Theory and Optical Fiber Devices and Systems covers Fourier theory and signal analysis over photonic components, including time lenses in optical communication. Sections cover wave propagation in optical waveguides based on Maxwell equations and the nonlinear Schrödinger equation. Optical Fourier transform in the form of time lens is covered, for example in modulation format conversion and spectrum magnification, and couplers and their use for optical discrete Fourier transformation are also discussed. Other important subjects are discussed such as shot noise, thermal noise and also the basics of four wave mixing in relation to time lenses. Detailed derivations and a deeper background for the chapters are provided in appendices where appropriate. Some of the theory is more generally applicable beyond optical communication and is of relevance also for communications engineering. The Fourier theory dimension of the book presents the relationship between Fourier series and Fourier integrals and also the related Laplace transform.

  • Fourier Transforms in NMR, Optical, and Mass Spectrometry

    A User's Handbook
    • 1st Edition
    • A.G. Marshall + 1 more
    • English
    Written by spectroscopists for spectroscopists, here is a book which is not only a valuable handbook and reference work, but also an ideal teaching text for Fourier transform methods as they are applied in spectroscopy. It offers the first unified treatment of the three most popular types of FT/spectroscopy, with uniform notation and complete indexing of specialized terms. All mathematics is self-contained, and requires only a knowledge of simple calculus. The main emphasis is on pictures and physical analogs rather than detailed algebra. Instructive problems, presented at the end of each chapter, offer extensions of the basic treatment. Solutions are given or outlined for all problems.The book offers a wealth of practical information to spectroscopists. Non-ideal effects are treated in detail: noise (source- and detector-limited); non-linear response; limits to spectrometer performance based on finite detection period, finite data size, mis-phasing, etc. Common puzzles and paradoxes are explained: e.g. use of mathematically complex variables to represent physically real quantities; interpretation of negative frequency signals; on-resonance vs. off-resonance response; interpolation (when it helps and when it doesn't); ultimate accuracy of the data; differences between linearly- and circularly-polarized radiation; multiplex advantage or disadvantage, etc.Chapter 1 introduces the fundamental line shapes encountered in spectroscopy, from a simple classical mass-on-a-spring model. The Fourier transform relationship between the time-domain response to a sudden impulse and the steady-state frequency-domain response (absorption and dispersion spectra) to a continuous oscillation is established and illustrated. Chapters 2 and 3 summarize the basic mathematics (definitions, formulas, theorems, and examples) for continuous (analog) and discrete (digital) Fourier transforms, and their practical implications. Experimental aspects which are common to the signal (Chapter 4) and noise (Chapter 5) in all forms of Fourier transform spectrometry are followed by separate chapters for treatment of those features which are unique to FT/MS, FT/optical, FT/NMR, and other types of FT/spectroscopy.The list of references includes both historical and comprehensive reviews and monographs, along with articles describing several key developments. The appendices provide instant access to FT integrals and fast algorithms as well as a pictorial library of common Fourier transform function pairs. The comprehensive index is designed to enable the reader to locate particular key words, including those with more than one name.

  • Weighted Norm Inequalities and Related Topics

    • 1st Edition
    • Volume 116
    • J. García-Cuerva + 1 more
    • English
    The unifying thread of this book is the topic of Weighted Norm Inequalities, but many other related topics are covered, including Hardy spaces, singular integrals, maximal operators, functions of bounded mean oscillation and vector valued inequalities. The emphasis is placed on basic ideas; problems are first treated in a simple context and only afterwards are further results examined.

  • Beyond Wavelets

    • 1st Edition
    • Volume 10
    • Grant Welland
    • English
    "Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago byMorlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering.Classica... wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach.However, with the current advances in science and technology, there is an immediate need to extend wavelet mathematical tools as well. "Beyond Wavelets" presents a list of ideas and mathematicalfoundati... for such extensions, including: continuous and digital ridgelets, brushlets, steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet frames, and quasi-affine wavelets. Wavelet subband algorithms are extended to pyramidal directional and nonuniform filter banks. In addition, this volume includes amethod for tomographic reconstruction using a mechanical image model and a statistical study for independent adaptive signal representation.Inves... already familiar with wavelet methods from areas such as engineering, statistics, and mathematics will benefit by owning this volume.

  • Introduction to Holomorphy

    • 1st Edition
    • Volume 106
    • J.A. Barroso
    • English
    This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.Infinite dimensional Holomorphy appears as a theory rich in fascinating problems and rich in applications to other branches of Mathematics and Mathematical Physics.

  • A Wavelet Tour of Signal Processing

    • 2nd Edition
    • Stephane Mallat
    • English
    This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris.

  • Fourier Acoustics

    Sound Radiation and Nearfield Acoustical Holography
    • 1st Edition
    • Earl G. Williams
    • English
    Intended a both a textbook and a reference, Fourier Acoustics develops the theory of sound radiation uniquely from the viewpoint of Fourier Analysis. This powerful perspective of sound radiation provides the reader with a comprehensive and practical understanding which will enable him or her to diagnose and solve sound and vibration problems in the 21st Century. As a result of this perspective, Fourier Acoustics is able to present thoroughly and simply, for the first time in book form, the theory of nearfield acoustical holography, an important technique which has revolutionised the measurement of sound. Relying little on material outside the book, Fourier Acoustics will be invaluable as a graduate level text as well as a reference for researchers in academia and industry.

  • Handbook of Fourier Transform Raman and Infrared Spectra of Polymers

    • 1st Edition
    • Volume 45
    • A.H. Kuptsov + 1 more
    • English
    A collection of infrared and Raman spectra of 500 natural and synthetic polymers of industrial importance is presented in this book. A large variety of compounds are included, starting with linear polyolefins and finishing with complex biopolymers and related compounds. The spectra were registered using Infrared Fourier Transform Spectrometers in the laboratory of the All-Russia Institute of Forensic Sciences. The IR and Raman spectra are presented together on the same sheet. The accompanying data include general and structure formulae, CAS register numbers, and sample preparation conditions.Features of this book:• Continues the long tradition of publishing specific and standard data of new chemical compounds.• For low-molecular weight substances, complementary IR and Raman spectra are featured on the same sample and printed on the same page. This "fingerprint" data allows the substance of the sample to be identified without doubt.• An important feature of this unique collection of data is the increase in the identification precision of unknown substances.• Peak tables are available in digital (ASCII) format, on a diskette delivered with the book. This allows the user to search for unknowns.• All the spectra in the collection are base-line corrected.This book will be of interest to scientists involved in the synthesis of new polymeric materials, polymer identification, and quality control. Libraries of scientific institutes, research centers, and universities involved in vibrational spectroscopy will also find this collection invaluable.

  • Fourier Analysis and Boundary Value Problems

    • 1st Edition
    • Enrique A. Gonzalez-Velasco
    • English
    Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.

  • Unitary Representations and Harmonic Analysis

    An Introduction
    • 2nd Edition
    • Volume 44
    • M. Sugiura
    • English
    The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

  • Recent Progress in Fourier Analysis

    • 1st Edition
    • Volume 111
    • I. Peral + 1 more
    • English

  • Fast Transforms Algorithms, Analyses, Applications

    • 1st Edition
    • Douglas F. Elliott + 1 more
    • English
    This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.

  • II: Fourier Analysis, Self-Adjointness

    • 1st Edition
    • Volume 2
    • Michael Reed + 1 more
    • English
    This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.