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From Fourier Analysis to Wavelets de Jonas Gomes

From Fourier Analysis to Wavelets: IMPA Monographs, cartea 3

Autor Jonas Gomes, Luiz Velho
en Limba Engleză Paperback – 22 oct 2016
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.
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Specificații

ISBN-13: 9783319370224
ISBN-10: 3319370227
Pagini: 210
Ilustrații: XIII, 210 p. 77 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.45 kg
Ediția:Softcover reprint of the original 1st ed. 2015
Editura: Springer International Publishing
Colecția Springer
Seria IMPA Monographs

Locul publicării:Cham, Switzerland

Cuprins

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.

Recenzii

“The authors present a short textbook about thefundamentals of Fourier analysis (such as Fourier series, Fourier transform,and windowed Fourier transform) and wavelet theory (such as continuous/discretewavelet transforms, multiresolution analysis, decomposition/reconstructionalgorithms, and construction of orthogonal/biorthogonal wavelets) with emphasison the underlying ideas. … This textbook is mainly written for students incomputer science, physics, and engineering.” (Manfred Tasche, zbMATH, Vol.1325.42001, 2016)

Textul de pe ultima copertă

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.

Caracteristici

Includes extensive appendices on Systems and Filters and the Z Transform Emphasis is given on ideas and intuition rather than heavy computations Provides great detail on different types of wavelets: Orthogonal Wavelets, Biorthogonal Wavelets, Wavelet Design, and Constructing Wavelets