Download or read book Fourier Hadamard and Hilbert Transforms in Chemistry written by Alan Marshall and published by Springer Science & Business Media. This book was released on 1982-02-01 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: In virtually all types of experiments in which a response is analyzed as a function of frequency (e. g. , a spectrum), transform techniques can significantly improve data acquisition and/or data reduct ion. Research-level nuclear magnet ic resonance and infra-red spectra are already obtained almost exclusively by Fourier transform methods, because Fourier transform NMR and IR spectrometers have been commercially available since the late 1960·s. Similar transform techniques are equally valuable (but less well-known) for a wide range of other chemical applications for which commercial instruments are only now becoming available: for example, the first corrmercial Fourier transform mass spectrometer was introduced this year (1981) by Nicolet Instrument Corporation. The purpose of this volume is to acquaint practicing chemists with the basis, advantages, and applica of Fourier, Hadamard, and Hilbert transforms in chemistry. For tions almost all chapters, the author is the investigator who was the first to apply such methods in that field. The basis and advantages of transform techniques are described in Chapter 1. Many of these aspects were understood and first applied by infrared astronomers in the 1950·s, in order to improve the otherwise unacceptably poor signal-to-noise ratio of their spec tra. However, the computations required to reduce the data were painfully slow, and required a 1 arge computer.

Download or read book Fourier Hadamard and Hilbert Transforms in Chemistry written by Alan Marshall and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: In virtually all types of experiments in which a response is analyzed as a function of frequency (e. g. , a spectrum), transform techniques can significantly improve data acquisition and/or data reduct ion. Research-level nuclear magnet ic resonance and infra-red spectra are already obtained almost exclusively by Fourier transform methods, because Fourier transform NMR and IR spectrometers have been commercially available since the late 1960·s. Similar transform techniques are equally valuable (but less well-known) for a wide range of other chemical applications for which commercial instruments are only now becoming available: for example, the first corrmercial Fourier transform mass spectrometer was introduced this year (1981) by Nicolet Instrument Corporation. The purpose of this volume is to acquaint practicing chemists with the basis, advantages, and applica of Fourier, Hadamard, and Hilbert transforms in chemistry. For tions almost all chapters, the author is the investigator who was the first to apply such methods in that field. The basis and advantages of transform techniques are described in Chapter 1. Many of these aspects were understood and first applied by infrared astronomers in the 1950·s, in order to improve the otherwise unacceptably poor signal-to-noise ratio of their spec tra. However, the computations required to reduce the data were painfully slow, and required a 1 arge computer.

Download or read book Fourier Hadamard and Hilbert Transforms in Chemistry written by Alan Marshall and published by Springer. This book was released on 2013-06-13 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: In virtually all types of experiments in which a response is analyzed as a function of frequency (e. g. , a spectrum), transform techniques can significantly improve data acquisition and/or data reduct ion. Research-level nuclear magnet ic resonance and infra-red spectra are already obtained almost exclusively by Fourier transform methods, because Fourier transform NMR and IR spectrometers have been commercially available since the late 1960·s. Similar transform techniques are equally valuable (but less well-known) for a wide range of other chemical applications for which commercial instruments are only now becoming available: for example, the first corrmercial Fourier transform mass spectrometer was introduced this year (1981) by Nicolet Instrument Corporation. The purpose of this volume is to acquaint practicing chemists with the basis, advantages, and applica of Fourier, Hadamard, and Hilbert transforms in chemistry. For tions almost all chapters, the author is the investigator who was the first to apply such methods in that field. The basis and advantages of transform techniques are described in Chapter 1. Many of these aspects were understood and first applied by infrared astronomers in the 1950·s, in order to improve the otherwise unacceptably poor signal-to-noise ratio of their spec tra. However, the computations required to reduce the data were painfully slow, and required a 1 arge computer.

Download or read book FOURIER HADAMARD AND HIBERT TRANSFORMS IN CHEMISTRY written by Alan G. Marshall and published by . This book was released on 1982 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fourier Meets Hilbert and Riesz written by René Erlin Castillo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-07-05 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction into the modern theory of classical harmonic analysis, dealing with Fourier analysis and the most elementary singular integral operators, the Hilbert transform and Riesz transforms. Ideal for self-study or a one semester course in Fourier analysis, included are detailed examples and exercises.

Download or read book Hilbert Transforms Volume 2 written by Frederick W. King and published by Cambridge University Press. This book was released on 2009-04-27 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive reference on Hilbert transforms covering the mathematical techniques for evaluating them, and their application.

Download or read book Fourier Transforms in NMR Optical and Mass Spectrometry written by A.G. Marshall and published by Elsevier. This book was released on 2016-02-25 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Certain Relationships Between Discrete Fourier and Hadamard Transforms written by Thomas Christopher Addison and published by . This book was released on 1970 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hilbert Huang Transform and Its Applications written by Norden Eh Huang and published by World Scientific. This book was released on 2005 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: The HilbertOCoHuang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the WignerOCoVille Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics OCo the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and visualization.

Download or read book Application of Hartley and Hilbert Transforms in Fourier Transform Ion Cyclotron Resonance Mass Spectrometry written by Christopher Paul Williams and published by . This book was released on 1992 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by McGraw-Hill Companies. This book was released on 1978 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematics for Physical Chemistry written by Robert G. Mortimer and published by Elsevier. This book was released on 2005-06-10 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data. Numerous examples and problems interspersed throughout the presentations Each extensive chapter contains a preview, objectives, and summary Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics

Download or read book The Fast Fourier Hadamard Transform and Its Use in Signal Representation and Classification written by J. E Whelchel (Jr) and published by . This book was released on 1968 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discrete time transform was studied and applied to the representation and discrimination of digitized signals. The transform consists of an orthogonal (Hadamard) matrix whose elements are all ones and minus ones. To facilitate implementation, a fast Hadamard transform (FHT) has been developed requiring only NlogN rather than N squared algebraic additions. Several properties of the FHT are revealed, including the nature of its presence in the fast Fourier transform, in which it performs the additive operations as shown by further decomposing the product of matrices representing the FFT.

Download or read book Fundamentals and Applications of Fourier Transform Mass Spectrometry written by Philippe Schmitt-Kopplin and published by Elsevier. This book was released on 2019-08-11 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals and Applications of Fourier Transform Mass Spectrometry is the first book to delve into the underlying principles on the topic and their linkage to industrial applications. Drs. Schmitt-Kopplin and Kanawati have brought together a team of leading experts in their respective fields to present this technique from many different perspectives, describing, at length, the pros and cons of FT-ICR and Orbitrap. Numerous examples help researchers decide which instruments to use for their particular scientific problem and which data analysis methods should be applied to get the most out of their data. Covers FT-ICR-MS and Orbitrap’s fundamentals, enhancing researcher knowledge Includes details on ion sources, data processing, chemical analysis and imaging Provides examples across the wide spectrum of applications, including omics, environmental, chemical, pharmaceutical and food analysis

Download or read book Fourier and Hilbert Transforms of Generalized Functions of One Real Variable written by R. W. Best and published by . This book was released on 1966 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Hilbert Transform of Schwartz Distributions and Applications written by J. N. Pandey and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern and up-to-date treatment of the Hilberttransform of distributions and the space of periodic distributions.Taking a simple and effective approach to a complex subject, thisvolume is a first-rate textbook at the graduate level as well as anextremely useful reference for mathematicians, applied scientists,and engineers. The author, a leading authority in the field, shares with thereader many new results from his exhaustive research on the Hilberttransform of Schwartz distributions. He describes in detail how touse the Hilbert transform to solve theoretical and physicalproblems in a wide range of disciplines; these include aerofoilproblems, dispersion relations, high-energy physics, potentialtheory problems, and others. Innovative at every step, J. N. Pandey provides a new definitionfor the Hilbert transform of periodic functions, which isespecially useful for those working in the area of signalprocessing for computational purposes. This definition could alsoform the basis for a unified theory of the Hilbert transform ofperiodic, as well as nonperiodic, functions. The Hilbert transform and the approximate Hilbert transform ofperiodic functions are worked out in detail for the first time inbook form and can be used to solve Laplace's equation with periodicboundary conditions. Among the many theoretical results proved inthis book is a Paley-Wiener type theorem giving thecharacterization of functions and generalized functions whoseFourier transforms are supported in certain orthants of Rn. Placing a strong emphasis on easy application of theory andtechniques, the book generalizes the Hilbert problem in higherdimensions and solves it in function spaces as well as ingeneralized function spaces. It simplifies the one-dimensionaltransform of distributions; provides solutions to thedistributional Hilbert problems and singular integral equations;and covers the intrinsic definition of the testing function spacesand its topology. The book includes exercises and review material for all majortopics, and incorporates classical and distributional problems intothe main text. Thorough and accessible, it explores new ways to usethis important integral transform, and reinforces its value in bothmathematical research and applied science. The Hilbert transform made accessible with many new formulas anddefinitions Written by today's foremost expert on the Hilbert transform ofgeneralized functions, this combined text and reference covers theHilbert transform of distributions and the space of periodicdistributions. The author provides a consistently accessibletreatment of this advanced-level subject and teaches techniquesthat can be easily applied to theoretical and physical problemsencountered by mathematicians, applied scientists, and graduatestudents in mathematics and engineering. Introducing many new inversion formulas that have been developedand applied by the author and his research associates, the book: * Provides solutions to the distributional Hilbert problem andsingular integral equations * Focuses on the Hilbert transform of Schwartz distributions,giving intrinsic definitions of the space H(D) and its topology * Covers the Paley-Wiener theorem and provides many importanttheoretical results of importance to research mathematicians * Provides the characterization of functions and generalizedfunctions whose Fourier transforms are supported in certainorthants of Rn * Offers a new definition of the Hilbert transform of the periodicfunction that can be used for computational purposes in signalprocessing * Develops the theory of the Hilbert transform of periodicdistributions and the approximate Hilbert transform of periodicdistributions * Provides exercises at the end of each chapter--useful toprofessors in planning assignments, tests, and problems

Download or read book Fourier Series and Hilbert Transforms of Functions with Values in UMD Banach Spaces written by José L. Rubio de Francia and published by . This book was released on 1983 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: