Near canonic double-based number system (DBNS) with applications in digital signal processing
Vassil S. Dimitrov, Saeid Sadeghi-Emamchaie, GRAHAM A. JULLIEN, W. C. Miller · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
In this paper we explore a new number system which uses a double base. The representation of the numbers has a very simple geometric interpretation, allowing potentially fast implementation of the basic arithmetic operations. The transformation of the integers into minimal form, however, leads to some problems associated with transcendental number theory, and we identify and open the discussion on these problems. An intriguing implementation vehicle, which has some of the properties associated with symbolic substitution in optical computing, is the use of Cellular Neural Network (CNNs) to perform digital reduction. Brief details are presented on CNN implementation, and a system-level example is shown in order to justify the applicability of the proposed theory in digital signal processing.