BEYOND BOOLE ALGEBRA WITH TMS320 DSP MULTIPROCESSING

From information compression study, we assumed the following outlines : i) Transmitted informational state is a quantized, serial, local data. ii) Nontransmitted informational state is a continuous, concurrent, distributed pattern. iii) It is possible to define properties of a "Super-Boole" computer matching these two kinds of information processing, combining bits and forms, i.e. arithmetic calculus and Boole algebra principles with harmonic analysis and Lie algebra.

In fact, these principles point out quantum calculus. But in the face of hardware difficulties making quantum computer, and software difficulties (calculation time) simulating with boolean computer, we suggest, to study these systems, a circuit diagram with DSP processors. Feasibility evaluation is proposed from fixed-point TMS320Cxx.

Independence scale principle may be applied. This principle of calculus does not modify the shape of a form, only its amplitude. So normalized FFT F1 is seen as NOT operator, convolution as OR, product as AND, normalized Dirac distribution d1(x) and 1(x) as boolean 0 and 1 respectively.

Hardware applications like timing, computational speed, wiring are examined. For instance, boolean operation XOR here means a new DSP operation, where signal and spectrum are multiplied. It is a new device for programming.

From separability of M-dimension FT property, it is possible to construct arithmetic acting on M-dimension numbers whose 'bits" are themselves signals of N-samples, with a very important new feature : there are two "zeroes", the real number "0" and the "super-boolean" zero normalized distribution d1. Other extensions of boolean calculus, as non-commutability and Lie algebra, modulation and modal logic, etc, are to be considered. The main advantage in relation to quantum computer is here it is extremely easy keeping coherence, with SYNC inputs.

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