From Fourier Analysis to Wavelets

From Fourier Analysis to Wavelets

by Jonas Gomes, Luiz Velho

Paperback(Softcover reprint of the original 1st ed. 2015)

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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.

Product Details

ISBN-13: 9783319370224
Publisher: Springer International Publishing
Publication date: 10/22/2016
Series: IMPA Monographs , #3
Edition description: Softcover reprint of the original 1st ed. 2015
Pages: 210
Product dimensions: 6.10(w) x 9.25(h) x (d)

Table of Contents

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.

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