Introduction into the Complex Haar like Transforms Based on Rotation Angles

2010
Peteris Misāns

A novel class of generalization of Haar like complex discrete unitary transforms is presented. The basics of the class of COmplex RABOT Haar transforms (CORA HT) are described. Additionally, three novel subclasses of CORA HT are introduced using restrictions on the values of angles. The subclasses differ by the diversity of values of rotation angles. The generalized Jacobi rotation matrix has been used for the building of transform matrices. Examples of shapes of basis function(s) (BF) are presented. Basic properties of BFs for several subclasses of transforms are described. Certain parts of given BFs are invariant to shifting. Recurrent formulas for the calculation of BFs are given. A generalized Kronecker product for the calculation of transform matrix has been used. An insertion of permutation matrices between factorized matrices ensures the ordering of BFs by ranks. The number of operations for the fast calculation of transforms is presented.

Atslēgas vārdi
Orthonormal Transforms, Parameterization of Transforms, Haar Functions, Generalization of Haar Functions

Misāns, P. Introduction into the Complex Haar like Transforms Based on Rotation Angles. Telekomunikācijas un elektronika. Nr.10, 2010, 1.-6.lpp. ISSN 1407-8880.

Publikācijas valoda
English (en)