1.

Record Nr.

UNINA9910300249703321

Autore

Gomes Jonas

Titolo

From Fourier Analysis to Wavelets / / by Jonas Gomes, Luiz Velho

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015

ISBN

3-319-22075-6

Edizione

[1st ed. 2015.]

Descrizione fisica

1 online resource (216 p.)

Collana

IMPA Monographs ; ; 3

Disciplina

510

Soggetti

Fourier analysis

Harmonic analysis

Signal processing

Image processing

Speech processing systems

Fourier Analysis

Abstract Harmonic Analysis

Signal, Image and Speech Processing

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

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.

Sommario/riassunto

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.