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＜E-Book＞
Foundations of Discrete Harmonic Analysis / by Vasily N. Malozemov, Sergey M. Masharsky
(Lecture Notes in Applied and Numerical Harmonic Analysis. ISSN:25127209)

Edition	1st ed. 2020.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2020
Language	English
Size	XV, 247 p. 21 illus., 1 illus. in color : online resource
Authors	*Malozemov, Vasily N author Masharsky, Sergey M author SpringerLink (Online service)
Subjects	LCSH:Mathematics -- Data processing  All Subject Search LCSH:Signal processing LCSH:Fourier analysis FREE:Computational Mathematics and Numerical Analysis FREE:Signal, Speech and Image Processing FREE:Fourier Analysis
Notes	1 Preliminaries -- 2 Signal Transforms -- 3 Spline Subspaces -- 4 Fast Algorithms -- Solutions -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-030-47048-7

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