國立虎尾科技大學 |

Foundations of Discrete Harmonic Analysis

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Foundations of Discrete Harmonic Analysis/ by Vasily N. Malozemov, Sergey M. Masharsky.
Author:	Malozemov, Vasily N.
other author:	Masharsky, Sergey M.
Description:	XV, 247 p. 21 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Computer mathematics. -
Online resource:	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. - 1st ed. 2020. - XV, 247 p. 21 illus., 1 illus. in color.online resource. - Lecture Notes in Applied and Numerical Harmonic Analysis,2512-6482. - Lecture Notes in 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:

1199796
Computer mathematics.

LC Class. No.: QA71-90

Dewey Class. No.: 518

Foundations of Discrete Harmonic Analysis
LDR:02604nam a22003975i 4500 001 1021988
003 DE-He213
005 20200704112059.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030470487 $9 978-3-030-47048-7
024 7 $a 10.1007/978-3-030-47048-7 $2 doi
035 $a 978-3-030-47048-7
050 4 $a QA71-90
072 7 $a PBKS $2 bicssc
072 7 $a MAT006000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 518 $2 23
100 1 $a Malozemov, Vasily N. $e author. $0 (orcid)0000-0003-0706-0578 $1 https://orcid.org/0000-0003-0706-0578 $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1317667
245 1 0 $a Foundations of Discrete Harmonic Analysis $h [electronic resource] / $c by Vasily N. Malozemov, Sergey M. Masharsky.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2020.
300 $a XV, 247 p. 21 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Lecture Notes in Applied and Numerical Harmonic Analysis, $x 2512-6482
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.
650 0 $a Computer mathematics. $3 1199796
650 0 $a Signal processing. $3 561459
650 0 $a Image processing. $3 557495
650 0 $a Speech processing systems. $3 564428
650 0 $a Fourier analysis. $3 639284
650 1 4 $a Computational Mathematics and Numerical Analysis. $3 669338
650 2 4 $a Signal, Image and Speech Processing. $3 670837
650 2 4 $a Fourier Analysis. $3 672627
700 1 $a Masharsky, Sergey M. $e author. $1 https://orcid.org/0000-0001-7647-1034 $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1317668
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030470470
776 0 8 $i Printed edition: $z 9783030470494
830 0 $a Lecture Notes in Applied and Numerical Harmonic Analysis, $x 2512-6482 $3 1264855
856 4 0 $u https://doi.org/10.1007/978-3-030-47048-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)