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＜電子ブック＞
From Fourier Analysis to Wavelets / by Jonas Gomes, Luiz Velho
(IMPA Monographs ; 3)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	XIII, 210 p. 77 illus : online resource
著者標目	*Gomes, Jonas author Velho, Luiz author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Harmonic analysis LCSH:Signal processing FREE:Fourier Analysis FREE:Abstract Harmonic Analysis FREE:Signal, Speech and Image Processing
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-22075-8

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