Fourier Transforms in Spectroscopy

Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers. Class-tested at Dartmouth Provides the same solid background as classic texts in the field, but with an emphasis on digital and other contemporary applications to signal and image processing Modular coverage of material allows for topics to be covered by preference MATLAB files and Solutions Manual available to instructors Over 300 figures, 200 worked examples, and 432 homework problems

Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership. The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs.

Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book’s attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.

'Spectroscopy in Catalysis' describes the most important modern analytical techniques used to investigate catalytic surfaces. These include electron spectroscopy (XPS, UPS, AES, EELS), ion spectroscopy (SIMS, SNMS, RBS, LEIS), vibrational spectroscopy (infrared, Raman, EELS), temperature-programmed techniques (TPR, TPO, TDS), diffraction (XRD, LEED, EXAFS), and microscopy (TEM, SEM, STEM, STM, AFM, FEM, and FIM). Each chapter uses current applications to illustrate the type of information that the technique provides and evaluates its possibilities and limitations. This second edition includes significant new developments, for example scanning probe microscopies, the imaging and vibrational techniques have been revised, the case studies expanded with an example on polymerization catalysts, and all the other chapters updated with recent examples and relevant new literature. From reviews of the First Edition: 'This is a truly valuable book … very useful for industrial practitioners who need to be aware of the type of information that can be obtained from modern surface spectroscopies .... The book has a superb pedagogic value…' Journal of Catalysis '… this is an excellent text on spectroscopies in catalysis and I highly recommend it for … introductory courses on heterogeneous catalysis or as a general introductory monograph.' Journal of the American Chemical Society

Superbly organized and of great pedagogic value, 'Spectroscopy in Catalysis' describes the most important modern analytical techniques used to investigate catalytic surfaces. These include electron, ion, and vibrational spectroscopy, mass spectrometry, temperature-programmed techniques, diffraction, and microscopy. With the focus on practical use, rather than theory, each chapter presents current applications to illustrate the type of information that the technique provides and evaluates its possibilities and limitations, allowing selection of the best catalyst and the correct technique to solve a given problem. This third edition includes significant new developments and case studies, with all the chapters updated by way of recent examples and relevant new literature. For students and for everyone who wants a digestible introduction to catalyst characterization. From reviews of the previous editions: 'This is a truly valuable book … very useful for industrial practitioners who need to be aware of the type of information that can be obtained from modern surface spectroscopies .... The book has a superb pedagogic value…' Journal of Catalysis '… this is an excellent text on spectroscopies in catalysis and I highly recommend it for … introductory courses on heterogeneous catalysis or as a general introductory monograph.' Journal of the American Chemical Society

Fourier Methods in Imaging introduces the mathematical tools for modeling linear imaging systems to predict the action of the system or for solving for the input. The chapters are grouped into five sections, the first introduces the imaging “tasks” (direct, inverse, and system analysis), the basic concepts of linear algebra for vectors and functions, including complex-valued vectors, and inner products of vectors and functions. The second section defines «special» functions, mathematical operations, and transformations that are useful for describing imaging systems. Among these are the Fourier transforms of 1-D and 2-D function, and the Hankel and Radon transforms. This section also considers approximations of the Fourier transform. The third and fourth sections examine the discrete Fourier transform and the description of imaging systems as linear «filters», including the inverse, matched, Wiener and Wiener-Helstrom filters. The final section examines applications of linear system models to optical imaging systems, including holography. Provides a unified mathematical description of imaging systems. Develops a consistent mathematical formalism for characterizing imaging systems. Helps the reader develop an intuitive grasp of the most common mathematical methods, useful for describing the action of general linear systems on signals of one or more spatial dimensions. Offers parallel descriptions of continuous and discrete cases. Includes many graphical and pictorial examples to illustrate the concepts. This book helps students develop an understanding of mathematical tools for describing general one- and two-dimensional linear imaging systems, and will also serve as a reference for engineers and scientists

This is the second edition of a unique book in the field of in vivo NMR covering in detail the technical and biophysical aspects of the technique. The contents of the book are appropriate to both beginners and experienced users of in vivo NMR spectroscopy. The new edition is focussed on bringing the reader practical insights and advice, but is also geared towards use as a study aid and in NMR courses. Recent advances in NMR spectroscopy, like high field NMR, hyperpolarized NMR and new localization and editing techniques have been included. An extensive and updated treatment of radiofrequency pulses is given, together with several tables and recipes for their generation. Solutions to the exercises within this text can be found here

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to: compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques perform a change of measure on the characteristic function in order to make the price process a martingale recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps. Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9

The authors describe basic theoretical concepts of vibrational spectroscopy, address instrumental aspects and experimental procedures, and discuss experimental and theoretical methods for interpreting vibrational spectra. It is shown how vibrational spectroscopy provides information on general aspects of proteins, such as structure, dynamics, and protein folding. In addition, the authors use selected examples to demonstrate the application of Raman and IR spectroscopy to specific biological systems, such as metalloproteins, and photoreceptors. Throughout, references to extensive mathematical and physical aspects, involved biochemical features, and aspects of molecular biology are set in boxes for easier reading. Ideal for undergraduate as well as graduate students of biology, biochemistry, chemistry, and physics looking for a compact introduction to this field.

Raman spectroscopy is the inelastic scattering of light by matter. Being highly sensitive to the physical and chemical properties of materials, as well as to environmental effects that change these properties, Raman spectroscopy is now evolving into one of the most important tools for nanoscience and nanotechnology. In contrast to usual microscopyrelated techniques, the advantages of using light for nanoscience relate to both experimental and fundamental aspects.