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Foundations of discrete harmonic ana...

Malozemov, Vasily N.

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Foundations of discrete harmonic analysis

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Foundations of discrete harmonic analysis/ by Vasily N. Malozemov, Sergey M. Masharsky.
作者:	Malozemov, Vasily N.
其他作者:	Masharsky, Sergey M.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xv, 247 p. :ill., digital ;24 cm.
內容註:	1 Preliminaries -- 2 Signal Transforms -- 3 Spline Subspaces -- 4 Fast Algorithms -- Solutions -- References -- Index.
Contained By:	Springer eBooks
標題:	Harmonic analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-47048-7
ISBN:	9783030470487

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

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

555704
Harmonic analysis.

LC Class. No.: QA403 / .M356 2020

Dewey Class. No.: 515.2433

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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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