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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.

Fourier analysis. --- Fourier transformations. --- Singular integrals. --- Wavelets (Mathematics). --- Fourier transformations --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analysis, Fourier --- Transformations, Fourier --- Transforms, Fourier --- Mathematics. --- Computer science --- Computer mathematics. --- Visualization. --- Mathematics --- Fourier Analysis. --- Mathematical Applications in Computer Science. --- Discrete Mathematics in Computer Science. --- Math Applications in Computer Science. --- Mathematics Education. --- Study and teaching. --- Mathematical analysis --- Fourier analysis --- Transformations (Mathematics) --- Computational complexity. --- Computer science. --- Math --- Science --- Informatics --- Complexity, Computational --- Electronic data processing --- Machine theory --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Computer science—Mathematics. --- Mathematics—Study and teaching . --- Computer mathematics

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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.

Optics. Quantum optics --- Artificial intelligence. Robotics. Simulation. Graphics --- Harmonic analysis. Fourier analysis --- Moiré method --- 535.4 --- 52 --- AA / International- internationaal --- Fringe method, Moiré --- Andere wetenschappen --- Diffraction gratings --- Materials --- Strains and stresses --- Testing --- Fourier analysis. --- Lasers. --- Photonics. --- Optical data processing. --- Applied mathematics. --- Engineering mathematics. --- Fourier Analysis. --- Optics, Lasers, Photonics, Optical Devices. --- Image Processing and Computer Vision. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- New optics --- Optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Analysis, Fourier --- Mathematics --- Optical equipment

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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.

Didactics of mathematics --- Harmonic analysis. Fourier analysis --- Discrete mathematics --- Mathematics --- Computer science --- Computer architecture. Operating systems --- Computer. Automation --- Fourieranalyse --- complexiteit --- discrete wiskunde --- visualisatie --- computers --- didactiek --- informatica --- wiskunde --- computerkunde

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This is a new, revised and updated edition of the original book by Isaac Amidror. It presents the most comprehensive and methodical work on the theory of the moiré phenomenon, providing a full general-purpose and application-independent exposition of this fascinating effect. Based on the Fourier theory, it leads the reader through the various phenomena which occur in the superposition of repetitive layers, both in the image and in the spectral domains. The first chapters of the book present the basic theory which covers the superposition of monochrome, periodic layers. In later chapters the theory is extended to the even more interesting cases of polychromatic moirés and moirés between repetitive, non-periodic layers. Throughout the whole text 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. This book is intended for students, scientists, engineers and any readers who wish to widen their knowledge of the moiré effect. It also offers a beautiful demonstration of the Fourier theory and its relationship with other fields of mathematics and science. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the Fourier theory.

Harmonic analysis. Fourier analysis --- Mathematics --- Electronics and optics of solids --- Computer. Automation --- beeldverwerking --- Fourieranalyse --- toegepaste wiskunde --- optica