Self-similarity in Walsh Functions

Abstract

A structure which can be divided into smaller and smaller pieces, each piece being an exact replica of the entire structure is called self-similar. The set of Walsh functions can be classified into distinct self-similar groups and subgroups where members of each subgroup exhibit self-similarity. After a brief discussion on the generation of higher order Walsh functions from lower order Walsh functions by an alternating process, a scheme for classification of Walsh functions into self-similar groups and subgroups is presented. Self-similarity in radial and annular Walsh functions and the correspondence between Walsh filters and Walsh functions are also discussed.