Discrete Harmonic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Harmonic Analysis write by Tullio Ceccherini-Silberstein. This book was released on 2018-06-21. Discrete Harmonic Analysis available in PDF, EPUB and Kindle. A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Discrete Fourier Analysis
Discrete Fourier Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Fourier Analysis write by M. W. Wong. This book was released on 2011-05-30. Discrete Fourier Analysis available in PDF, EPUB and Kindle. This textbook presents basic notions and techniques of Fourier analysis in discrete settings. Written in a concise style, it is interlaced with remarks, discussions and motivations from signal analysis. The first part is dedicated to topics related to the Fourier transform, including discrete time-frequency analysis and discrete wavelet analysis. Basic knowledge of linear algebra and calculus is the only prerequisite. The second part is built on Hilbert spaces and Fourier series and culminates in a section on pseudo-differential operators, providing a lucid introduction to this advanced topic in analysis. Some measure theory language is used, although most of this part is accessible to students familiar with an undergraduate course in real analysis. Discrete Fourier Analysis is aimed at advanced undergraduate and graduate students in mathematics and applied mathematics. Enhanced with exercises, it will be an excellent resource for the classroom as well as for self-study.
Discrete Harmonic Analysis
Discrete Harmonic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Harmonic Analysis write by Tullio Ceccherini-Silberstein. This book was released on 2018-06-21. Discrete Harmonic Analysis available in PDF, EPUB and Kindle. This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.
Foundations of Discrete Harmonic Analysis
Foundations of Discrete Harmonic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Foundations of Discrete Harmonic Analysis write by Vasily N. Malozemov. This book was released on 2020-06-24. Foundations of Discrete Harmonic Analysis available in PDF, EPUB and Kindle. This book provides an introduction to discrete harmonic analysis (DHA) with a view towards applications to digital signal processing. In a nutshell, DHA is used to determine the time-frequency structure of a digitized signal, providing a representation of the signal as a sum of spectral components that can then be analyzed. The main methods of DHA are discrete Fourier transform and other discrete orthogonal transforms such as the Walsh and Haar transforms. Fast algorithms are used to process signals in real time, while additional options are provided by spline harmonic analysis. These topics are carefully covered in the book. With only modest prerequisites, some of which are recalled at the beginning, a profound mathematical theory is built almost from scratch. The 150 exercises included form an integral part of the text. Based decades of teaching experience, this book provides a basis for lecture courses starting at the upper undergraduate level, and will also prove a valuable resource for mathematicians and engineers interested in digital signal processing.
Discrete Tomography
Discrete Tomography - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Discrete Tomography write by Gabor T. Herman. This book was released on 1999-11. Discrete Tomography available in PDF, EPUB and Kindle. Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi croscopy to determine the presenceor absence ofatoms in crystallinestruc tures, which is again a two-valued situation.
