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Foundations of discrete harmonic ana...

Malozemov, Vasily N.

Foundations of discrete harmonic analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Foundations of discrete harmonic analysisby Vasily N. Malozemov, Sergey M. Masharsky.
Author:	Malozemov, Vasily N.
other author:	Masharsky, Sergey M.
Published:	Cham :Springer International Publishing :2020.
Description:	xv, 247 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Harmonic analysis.
Online resource:	https://doi.org/10.1007/978-3-030-47048-7
ISBN:	9783030470487$q(electronic bk.)

Foundations of discrete harmonic analysis
Malozemov, Vasily N.

Foundations of discrete harmonic analysis[electronic resource] /by Vasily N. Malozemov, Sergey M. Masharsky. - Cham :Springer International Publishing :2020. - xv, 247 p. :ill., digital ;24 cm. - Applied and numerical harmonic analysis,2296-5009. - Applied and numerical harmonic analysis..

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.

ISBN: 9783030470487$q(electronic bk.)

Standard No.: 10.1007/978-3-030-47048-7doiSubjects--Topical Terms:

189705
Harmonic analysis.

LC Class. No.: QA403 / .M356 2020

Dewey Class. No.: 515.2433

Foundations of discrete harmonic analysis
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245 1 0 $a Foundations of discrete harmonic analysis $h [electronic resource] / $c by Vasily N. Malozemov, Sergey M. Masharsky.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
300 $a xv, 247 p. : $b ill., digital ; $c 24 cm.
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505 0 $a 1 Preliminaries -- 2 Signal Transforms -- 3 Spline Subspaces -- 4 Fast Algorithms -- Solutions -- References -- Index.
520 $a 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.
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