國立高雄大學圖資館 |

Language: English

Back

The XFT quadrature in discrete Fouri...

Campos, Rafael G.

The XFT quadrature in discrete Fourier analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	The XFT quadrature in discrete Fourier analysisby Rafael G. Campos.
Author:	Campos, Rafael G.
Published:	Cham :Springer International Publishing :2019.
Description:	xiii, 235 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Fourier analysis.
Online resource:	https://doi.org/10.1007/978-3-030-13423-5
ISBN:	9783030134235$q(electronic bk.)

The XFT quadrature in discrete Fourier analysis
Campos, Rafael G.

The XFT quadrature in discrete Fourier analysis[electronic resource] /by Rafael G. Campos. - Cham :Springer International Publishing :2019. - xiii, 235 p. :ill., digital ;24 cm. - Applied and numerical harmonic analysis,2296-5009. - Applied and numerical harmonic analysis..

Introduction -- The ordinary discrete Fourier transform -- XFT: A discrete Fourier transform -- Applications of the XFT -- A discrete fractional Fourier transform.

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book's second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.

ISBN: 9783030134235$q(electronic bk.)

Standard No.: 10.1007/978-3-030-13423-5doiSubjects--Topical Terms:

184626
Fourier analysis.

LC Class. No.: QA403.5 / .C367 2019

Dewey Class. No.: 515.2433

The XFT quadrature in discrete Fourier analysis
LDR:02195nmm a2200337 a 4500 001 559029
003 DE-He213
005 20191030140737.0
006 m d
007 cr nn 008maaau
008 191219s2019 gw s 0 eng d
020 $a 9783030134235$q(electronic bk.)
020 $a 9783030134228$q(paper)
024 7 $a 10.1007/978-3-030-13423-5 $2 doi
035 $a 978-3-030-13423-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA403.5 $b .C367 2019
072 7 $a PBKF $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.2433 $2 23
090 $a QA403.5 $b .C198 2019
100 1 $a Campos, Rafael G. $3 841904
245 1 4 $a The XFT quadrature in discrete Fourier analysis $h [electronic resource] / $c by Rafael G. Campos.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xiii, 235 p. : $b ill., digital ; $c 24 cm.
490 1 $a Applied and numerical harmonic analysis, $x 2296-5009
505 0 $a Introduction -- The ordinary discrete Fourier transform -- XFT: A discrete Fourier transform -- Applications of the XFT -- A discrete fractional Fourier transform.
520 $a This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book's second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.
650 0 $a Fourier analysis. $3 184626
650 1 4 $a Special Functions. $3 274846
650 2 4 $a Real Functions. $3 273779
650 2 4 $a Integral Transforms, Operational Calculus. $3 275781
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Applied and numerical harmonic analysis. $3 558836
856 4 0 $u https://doi.org/10.1007/978-3-030-13423-5
950 $a Mathematics and Statistics (Springer-11649)