05466nam 2200721 a 450 991014331550332120210209155236.01-280-84769-797866108476930-470-61249-50-470-39462-51-84704-581-2(CKB)1000000000335551(EBL)700741(OCoLC)769341528(SSID)ssj0000313009(PQKBManifestationID)11222644(PQKBTitleCode)TC0000313009(PQKBWorkID)10358140(PQKB)10565906(MiAaPQ)EBC700741(CaSebORM)9781905209316(MiAaPQ)EBC261987(Au-PeEL)EBL261987(CaONFJC)MIL84769(OCoLC)936813939(EXLCZ)99100000000033555120061003d2007 uy 0engur|n|---|||||txtccrWavelets and their applications[electronic resource] /edited by Michel Misiti ... [et al.]1st editionLondon ;Newport Beach, CA ISTE20071 online resource (354 p.)ISTE ;v.668"Part of this book adapted from "Les ondelettes et leurs applications" published in France by Hermes Science/Lavoisier in 2003."--T.p. verso.1-905209-31-2 Includes bibliographical references (p. [321]-327) and index.Wavelets and their Applications; Table of Contents; Notations; Introduction; Chapter 1. A Guided Tour; 1.1. Introduction; 1.2. Wavelets; 1.2.1. General aspects; 1.2.2. A wavelet; 1.2.3. Organization of wavelets; 1.2.4. The wavelet tree for a signal; 1.3. An electrical consumption signal analyzed by wavelets; 1.4. Denoising by wavelets: before and afterwards; 1.5. A Doppler signal analyzed by wavelets; 1.6. A Doppler signal denoised by wavelets; 1.7. An electrical signal denoised by wavelets; 1.8. An image decomposed by wavelets; 1.8.1. Decomposition in tree form1.8.2. Decomposition in compact form1.9. An image compressed by wavelets; 1.10. A signal compressed by wavelets; 1.11. A fingerprint compressed using wavelet packets; Chapter 2. Mathematical Framework; 2.1. Introduction; 2.2. From the Fourier transform to the Gabor transform; 2.2.1. Continuous Fourier transform; 2.2.2. The Gabor transform; 2.3. The continuous transform in wavelets; 2.4. Orthonormal wavelet bases; 2.4.1. From continuous to discrete transform; 2.4.2. Multi-resolution analysis and orthonormal wavelet bases; 2.4.3. The scaling function and the wavelet; 2.5. Wavelet packets2.5.1. Construction of wavelet packets2.5.2. Atoms of wavelet packets; 2.5.3. Organization of wavelet packets; 2.6. Biorthogonal wavelet bases; 2.6.1. Orthogonality and biorthogonality; 2.6.2. The duality raises several questions; 2.6.3. Properties of biorthogonal wavelets; 2.6.4. Semi-orthogonal wavelets; Chapter 3. From Wavelet Bases to the Fast Algorithm; 3.1. Introduction; 3.2. From orthonormal bases to the Mallat algorithm; 3.3. Four filters; 3.4. Efficient calculation of the coefficients; 3.5. Justification: projections and twin scales; 3.5.1. The decomposition phase3.5.2. The reconstruction phase3.5.3. Decompositions and reconstructions of a higher order; 3.6. Implementation of the algorithm; 3.6.1. Initialization of the algorithm; 3.6.2. Calculation on finite sequences; 3.6.3. Extra coefficients; 3.7. Complexity of the algorithm; 3.8. From 1D to 2D; 3.9. Translation invariant transform; 3.9.1. ε -decimated DWT; 3.9.2. Calculation of the SWT; 3.9.3. Inverse SWT; Chapter 4. Wavelet Families; 4.1. Introduction; 4.2. What could we want from a wavelet?; 4.3. Synoptic table of the common families; 4.4. Some well known families4.4.1. Orthogonal wavelets with compact support4.4.1.1. Daubechies wavelets: dbN; 4.4.1.2. Symlets: symN; 4.4.1.3. Coiflets: coifN; 4.4.2. Biorthogonal wavelets with compact support: bior; 4.4.3. Orthogonal wavelets with non-compact support; 4.4.3.1. The Meyer wavelet: meyr; 4.4.3.2. An approximation of the Meyer wavelet: dmey; 4.4.3.3. Battle and Lemarié wavelets: btlm; 4.4.4. Real wavelets without filters; 4.4.4.1. The Mexican hat: mexh; 4.4.4.2. The Morlet wavelet: morl; 4.4.4.3. Gaussian wavelets: gausN; 4.4.5. Complex wavelets without filters; 4.4.5.1. Complex Gaussian wavelets: cgau4.4.5.2. Complex Morlet wavelets: cmorlThe last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression.ISTEWavelets (Mathematics)Electronic books.Wavelets (Mathematics)515.2433515/.2433Misiti Michel978944Misiti Michel978944MiAaPQMiAaPQMiAaPQBOOK9910143315503321Wavelets and their applications2231452UNINA