Fourier Transforms In Nmr Optical And Mass Spectrometry

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.

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.

This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical point of view. Some aspects, linear prediction for example, are explained here thoroughly for the first time.

Pulse and Fourier Transform NMR: Introduction to Theory and Methods presents the different types of pulse experiments that are commonly used and provides the theoretical background necessary for understanding these techniques. This book evaluates the practical application of pulse methods and the necessary instrumentation. Organized into seven chapters, this book begins with an overview of the NMR fundamentals and the basic pulse methods. This text then summarizes the important features of pulse spectrometers. Other chapters consider the rationale, the advantages, and the limitations of Fourier transform NMR methods. This book discusses as well how the idea of the rotating frame can be utilized to understand certain experiments that extend the range of application of pulse methods. The final chapter deals with a few significant special uses of pulse techniques. This book is a valuable resource for chemists and readers who are familiar with high resolution NMR but with no background in pulse methods.

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.

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

The application of the Fourier transform is being seen to an increasing extent in all branches of chemistry, but it is in the area of chemical analysis that the greatest activity is taking place. Fourier transform infrared and nuclear magnetic resonance spectrometry are already routine methods for obtaining high-sensitivity IR and NMR spectra. Analogous methods are now being developed for mass spectrometry (Fourier transform ion cyclo tron resonance spectrometry) and microwave spectroscopy, and Fourier transform techniques have been successfully applied in several areas of electrochemistry. In addition the fast Fourier transform algorithm has been used for smoothing, interpolation, and more efficient storage of data, and has been studied as a potential method for more efficient identification of samples using pattern recognition techniques. Linear transforms have also been shown to be useful in analytical chemistry. Probably the most important of these is the Hadamard transform, which has been applied in alternative methods for obtaining IR and NMR data at high sensitivity. Even though measurements involving this algorithm will probably not be applied as universally as their Fourier transform ana logs, in the area of pattern recognition application of the Hadamard trans form will in all probability prove more important than application of the Fourier transform.

Providing a definitive reference source on novel methods in NMR acquisition and processing, this book will highlight similarities and differences between emerging approaches and focus on identifying which methods are best suited for different applications. The highly qualified editors have conducted extensive research into the fundamentals of fast methods of data acquisition in NMR, including applications of non-Fourier methods of spectrum analysis. With contributions from additional distinguished experts in allied fields, clear explanations are provided on methods that speed up NMR experiments using different ways to manipulate the nuclei in the sample, modern methods for estimating the spectrum from the time domain response recorded during an NMR experiment, and finally how the data is sampled. Starting with a historical overview of Fourier Transformation and its role in modern NMR spectroscopy, this volume will clarify and demystify this important emerging field for spectroscopists and analytical chemists in industry and academia.