Pseudo-Boolean Matrix Techniques for State Minimisation of Finite State Machine Realisations of DSP Systems

Knoll, A. C.; Dooley, L. S. and Hetzheim, H. (1992). Pseudo-Boolean Matrix Techniques for State Minimisation of Finite State Machine Realisations of DSP Systems. In: Third IMA Conference on Mathematics in Signal Processing, 15-17 Dec 1992, Warwick, UK.

URL: http://www.ima.org.uk/Conferences/signal_processin...

Abstract

It is explored the mathematical basis of state reduction techniques, which have been developed in the design of Minimum Complexity Finite State Machines. The technique is based upon using first or second order Markovian Models and Pseudo-Boolean Matrices, to minimise the requisite number of states to implement IIR and FIR Digital Filters as well as DFT algorithms. The Boolean and the double Boolean Difference factors are then calculated to provide a measure of dependancy of state transitions for different arities. Rules are being developed for the connection of Pseudo-Boolean Matrices for different nodes and loops.

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