Complex Daubechies Wavelets

✍ Scribed by Jean-Marc Lina; Michel Mayrand

• Book ID: 102965477
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 673 KB
• Volume: 2
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1006/acha.1995.1015

✦ Synopsis

Using a parameterization of the space of multiresolution analyses with compact support ([-J, J+1]) and a maximum of (J) vanishing moments for the wavelet, this work investigates the general solution of the orthogonality conditions. More specifically, complex solutions up to (J=5) are presented. A classification of the solutions according to the degree of symmetry of the associated scaling function is proposed. Furthermore, symmetric but complex multiresolution analyses are described for a number of vanishing moments up to (J=8). Finally, a symmetric multiresolution analysis is constructed on ([0,1]). (C) 1995 Academic Press. Inc.