Walsh Function Systems: The Bisectional Evolutional Generation Pattern
In this paper, the concept of evolution is introduced to examine the generation process for Walsh function systems. By considering the generation process for Walsh function systems as the evolution process of certain discrete dynamic systems, a new unified generation pattern which is called the Bisectional Evolutional Generation Pattern (BEGP for short) for Walsh function systems is proposed, combined with their properties of symmetric copying. As a byproduct of this kind of pattern, a kind of ordering for Walsh function systems which is called quasi-Hadamard ordering is found naturally.
KeywordsWalsh function Quasi-Hadamard ordering Bisectional Evolutional Pattern Symmetric copying
Unable to display preview. Download preview PDF.
- 2.Wang, N.: Walsh Function Generated with Evolution. Journal of Image and Graphics 3, 225–231 (1996)Google Scholar
- 3.Wang, N.: The Mathematical Beauty of Walsh Functions (I). Journal of Yunnan University (19 supp.), 306–314 (1997)Google Scholar
- 4.Wang, N.: The Mathematical Beauty of Walsh Functions (II). Journal of Yunnan University (19 supp.), 315–323 (1997)Google Scholar
- 5.Falkowski, B.J., Perkowski, M.A.: Algorithms and Architecture for Gray Code Ordered Fast Walsh Transform. In: Proc. IEEE Int. Symp. Circ. & Syst (23rd ISCAS), New Orleans, USA, pp. 2913–1916 (1990)Google Scholar