LEADER 05397nam 2200697 a 450 001 996216942303316 005 20210209155236.0 010 $a1-280-84769-7 010 $a9786610847693 010 $a0-470-61249-5 010 $a0-470-39462-5 010 $a1-84704-581-2 035 $a(CKB)1000000000335551 035 $a(EBL)700741 035 $a(SSID)ssj0000313009 035 $a(PQKBManifestationID)11222644 035 $a(PQKBTitleCode)TC0000313009 035 $a(PQKBWorkID)10358140 035 $a(PQKB)10565906 035 $a(MiAaPQ)EBC700741 035 $a(MiAaPQ)EBC261987 035 $a(Au-PeEL)EBL261987 035 $a(CaONFJC)MIL84769 035 $a(OCoLC)501315925 035 $a(CaSebORM)9781905209316 035 $a(EXLCZ)991000000000335551 100 $a20061003d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aWavelets and their applications$b[electronic resource] /$fedited by Michel Misiti ... [et al.] 205 $a1st edition 210 $aLondon ;$aNewport Beach, CA $cISTE$d2007 215 $a1 online resource (354 p.) 225 1 $aISTE ;$vv.668 300 $a"Part of this book adapted from "Les ondelettes et leurs applications" published in France by Hermes Science/Lavoisier in 2003."--T.p. verso. 311 $a1-905209-31-2 320 $aIncludes bibliographical references (p. [321]-327) and index. 327 $aWavelets 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 form 327 $a1.8.2. 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 packets 327 $a2.5.1. 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 phase 327 $a3.5.2. 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. ? -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 families 327 $a4.4.1. 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 Lemarie? 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: cgau 327 $a4.4.5.2. Complex Morlet wavelets: cmorl 330 $aThe last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction. Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering. As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression. 410 0$aISTE 606 $aWavelets (Mathematics) 615 0$aWavelets (Mathematics) 676 $a515.2433 676 $a515/.2433 700 $aMisiti$b Michel$0978944 701 $aMisiti$b Michel$0978944 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996216942303316 996 $aWavelets and their applications$92231452 997 $aUNISA