From Fourier Analysis to Wavelets

ISBN-13: 9783319370224 / Angielski / Miękka / 2016 / 210 str.

Jonas Gomes; Luiz Velho

Opis

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.

Recenzje

"The authors present a short textbook about the fundamentals of Fourier analysis (such as Fourier series, Fourier transform, and windowed Fourier transform) and wavelet theory (such as continuous/discrete wavelet transforms, multiresolution analysis, decomposition/reconstruction algorithms, and construction of orthogonal/biorthogonal wavelets) with emphasis on the underlying ideas. ... This textbook is mainly written for students in computer science, physics, and engineering." (Manfred Tasche, zbMATH, Vol. 1325.42001, 2016)

Spis treści

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.

Blurb

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.