Mastering The Discrete Fourier Transform In One Two Or Several Dimensions
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Mastering the Discrete Fourier Transform in One, Two or Several Dimensions
Author: Isaac Amidror
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-07-19
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.
The Geometry of the Moiré Effect in One, Two, and Three Dimensions
Author: Vladimir Saveljev
language: en
Publisher: Cambridge Scholars Publishing
Release Date: 2022-06-15
The book describes not only 2D moiré patterns, but also explores the moiré effect in other dimensions, such as 1D and 3D (volumetric moiré patterns). It also explains the time-dependent moiré effect, including its spectral trajectories. The book features various illustrations and examples which will help the reader to identify the moiré effect and to distinguish it from other similar-looking effects. It will allow the reader to evaluate moiré patterns in particular circumstances, to establish control over the moiré effect, and to use it in modern technologies.
Essential Mathematics for NMR and MRI Spectroscopists
Author: Keith C Brown
language: en
Publisher: Royal Society of Chemistry
Release Date: 2020-08-28
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.