Unateness Properties of and-Exclusive-or Logic Circuits
IEEE Transactions on Computers
Techniques for the Transformation of Logic Equations
IEEE Transactions on Computers
A Generalized Technique for Spectral Analysis
IEEE Transactions on Computers
Real-Time Walsh-Hadamard Transformation
IEEE Transactions on Computers
A Compact Definition of Walsh Functions
IEEE Transactions on Computers
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The frequency of occurrence of logic functions of binary N-tuples can be observed from sequences of binary patterns. The logic functions considered here are AND, NOR, NAND, OR, and an odd-even parity check; and the frequency parameters are expressed as real matrix transformations on the probabilities of the patterns. Some properties, inverses, and interrelationships among the parameter sets are given, along with fast algorithms to facilitate computational processes. The results permit the outputs of convenient hardware logic operations to be converted into other parameters for smoothing, detection, or inference purposes, or to estimate the pattern probabilities by inversion. A measure of association among binary patterns is given as one characteristic feature which can be derived from the observed parameters.