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From Fourier analysis to wavelets

Gomes, Jonas.

From Fourier analysis to wavelets

Record Type:	Electronic resources : Monograph/item
Title/Author:	From Fourier analysis to waveletsby Jonas Gomes, Luiz Velho.
Author:	Gomes, Jonas.
other author:	Velho, Luiz.
Published:	Cham :Springer International Publishing :2015.
Description:	xiii, 210 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Wavelets (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-22075-8
ISBN:	9783319220758$q(electronic bk.)

From Fourier analysis to wavelets
Gomes, Jonas.

From Fourier analysis to wavelets[electronic resource] /by Jonas Gomes, Luiz Velho. - Cham :Springer International Publishing :2015. - xiii, 210 p. :ill., digital ;24 cm. - IMPA monographs ;v.3. - IMPA monographs ;v.2..

Introduction -- Function Representation and Reconstruction -- The Fourier Transform -- Windowed Fourier Transform -- The Wavelet Transform -- Multiresolution Representation -- The Fast Wavelet Transform -- Filter Banks and Multiresolution -- Constructing Wavelets -- Wavelet Design -- Orthogonal Wavelets -- Biorthogonal Wavelets -- Directions and Guidelines -- Appendices.

This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

ISBN: 9783319220758$q(electronic bk.)

Standard No.: 10.1007/978-3-319-22075-8doiSubjects--Topical Terms:

182734
Wavelets (Mathematics)

LC Class. No.: QA403.3

Dewey Class. No.: 515.2433

From Fourier analysis to wavelets
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245 1 0 $a From Fourier analysis to wavelets $h [electronic resource] / $c by Jonas Gomes, Luiz Velho.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xiii, 210 p. : $b ill., digital ; $c 24 cm.
490 1 $a IMPA monographs ; $v v.3
505 0 $a Introduction -- Function Representation and Reconstruction -- The Fourier Transform -- Windowed Fourier Transform -- The Wavelet Transform -- Multiresolution Representation -- The Fast Wavelet Transform -- Filter Banks and Multiresolution -- Constructing Wavelets -- Wavelet Design -- Orthogonal Wavelets -- Biorthogonal Wavelets -- Directions and Guidelines -- Appendices.
520 $a This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
650 0 $a Wavelets (Mathematics) $3 182734
650 0 $a Fournier analysis. $3 731745
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650 2 4 $a Signal, Image and Speech Processing. $3 273768
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856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22075-8
950 $a Mathematics and Statistics (Springer-11649)