Mastering the Discrete Fourier Transform in One, Two or Several Dimensions
Mastering the Discrete Fourier Transform in One, Two or Several Dimensions

Author: Isaac Amidror

Publisher: Springer Science & Business Media

Published: 2013-07-19

Total Pages: 388

ISBN-13: 1447151674

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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.

New Trends in Applied Harmonic Analysis
New Trends in Applied Harmonic Analysis

Author: Akram Aldroubi

Publisher: Birkhäuser

Published: 2016-04-21

Total Pages: 356

ISBN-13: 3319278738

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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.

Essential Mathematics for NMR and MRI Spectroscopists
Essential Mathematics for NMR and MRI Spectroscopists

Author: Keith C Brown

Publisher: Royal Society of Chemistry

Published: 2020-08-28

Total Pages: 884

ISBN-13: 1839162961

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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.

Operator-Related Function Theory and Time-Frequency Analysis
Operator-Related Function Theory and Time-Frequency Analysis

Author: Karlheinz Gröchenig

Publisher: Springer

Published: 2014-11-25

Total Pages: 204

ISBN-13: 3319085573

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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.

Landscapes of Time-Frequency Analysis
Landscapes of Time-Frequency Analysis

Author: Paolo Boggiatto

Publisher: Springer

Published: 2019-01-30

Total Pages: 358

ISBN-13: 3030052109

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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.

Mobile Networks for Biometric Data Analysis
Mobile Networks for Biometric Data Analysis

Author: Massimo Conti

Publisher: Springer

Published: 2016-07-27

Total Pages: 318

ISBN-13: 3319397001

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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.

Bode’s Law and the Discovery of Juno
Bode’s Law and the Discovery of Juno

Author: Clifford J. Cunningham

Publisher: Springer

Published: 2017-06-02

Total Pages: 309

ISBN-13: 3319328751

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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.

The Theory of the Moiré Phenomenon
The Theory of the Moiré Phenomenon

Author: Isaac Amidror

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 492

ISBN-13: 940114205X

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Who has not noticed, on one o~casion or another, those intriguing geometric patterns which appear at the intersection Of repetitive structures such as two far picket fences on a hill, the railings on both sides of a bridge, superposed layers of fabric, or folds of a nylon curtain? This fascinating phenomenon, known as the moire effect, has found useful applications in several fields of science and technology, such as metrology, strain analysis or even document authentication and anti-counterfeiting. However, in other situations moire patterns may have an unwanted, adverse effect. This is the case in the printing world, and, in particular, in the field of colour reproduction: moire patterns which may be caused by the dot-screens used for colour printing may severely deteriorate the image quality and tum into a real printer's nightmare. The starting point of the work on which this book is based was, indeed, in the research of moire phenomena in the context of the colour printing process. The initial aim of this research was to understand the nature and the causes of the superposition moire patterns between regular screens in order to find how to avoid, or at least minimize, their adverse effect on colour printing. This interesting research led us, after all, to a much more far reaching mathematical understanding of the moire phenomenon, whose interest stands in its own right, independently of any particular application.

Control of Color Imaging Systems
Control of Color Imaging Systems

Author: Lalit K. Mestha

Publisher: CRC Press

Published: 2018-10-03

Total Pages: 696

ISBN-13: 1420019430

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A Complete One-Stop Resource While digital color is now the technology of choice for printers, the knowledge required to address the quality and productivity issues of these devices is scattered across several technologies, as is its supporting literature. Bringing together information from diverse fields, Control of Color Imaging Systems: Analysis and Design is the first book to provide comprehensive coverage of the fundamentals and algorithms of the numerous disciplines associated with digital color printing in a single resource. The authors review the history of digital printing systems, explore its current status, and explain fundamental concepts, including: digital image formation, sampling, quantization, image coding, spot color calibration, and one- and multi-dimensional tone control of color management systems — including process physics and controls. A Complete Self-Tutorial With Over 150 Design Examples and 120 Exercise Problems Based on the authors’ three decades of hands-on technical and teaching experience, the text provides engineers and technicians with an end-to-end understanding of the color printing process, and helps them build a foundation drawn from the diverse disciplines needed to manage and control digital production printers. The control theory and methods presented in this book are state-of-the art for color printing systems; however, coverage of theoretical concepts and mathematics are kept to the basics, as the book is designed to teach hand’s on skills that will allow practitioners to gain an immediate understanding of quality and productivity concerns. The understanding provided will help practitioners build the technical skills needed to help pioneer the next generation of ideas, algorithms, and methods that will further expand the frontier of this rapidly evolving technology.