A Near Canonic Double-Based Number System (DBNS) with Applications in Digital Signal Processing

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 Networks (CNNs) to perform digit 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.