Introduction into the Haar Like Transforms Based on Rotation Angles

2007
Peteris Misāns

A novel class of generalization of Haar like discrete orthonormal functions is presented. The basics of the class of RABOT Haar transforms (RA HT) are described. Additionally, three novel subclasses of RA HT are introduced using restrictions on the values of angles. The subclasses differ by the diversity of values of rotation angles. Examples of shapes of basis function(s) (BF) are presented. Basic properties of BFs for two subclasses of transforms are described. Certain parts of given BFs are invariant to shifting. Recurrent formulas for the calculation of BFs are given. An insertion of permutation matrices between factorized matrices ensures the ordering of BFs by ranks. The rules for the building of permutation matrices are formulated. The number of operations for the fast calculation of transforms is presented.

Keywords
Orthonormal Transforms, Parameterization of Transforms, Haar Functions, Generalization of Haar Functions

Misāns, P. Introduction into the Haar Like Transforms Based on Rotation Angles. Telecommunications and Electronics. Vol.7, 2007, pp.6-13. ISSN 1407-8880.

Publication language
English (en)