PROPERTIES AND WAYS OF CALCULATION OF MULTIPOLARITY GENERALIZED WALSHTRANSFORMS

A new formulation of the Multi-Polarity Generalized Walsh Transform ha s been introduced. The formulation allows a uniform representation of Boolean functions by a set of orthogonal and generalized Walsh spectra l coefficients. Forward and inverse transformation kernels and the met hod of recursive generation of transform matrices by using Kronecker p roducts of elementary matrices have been given. Mutual relations among transform matrices and spectra for arbitrary polarities have been inv estigated. Fast Forward and Inverse Generalized Walsh Transforms have been developed. An algorithm to calculate the Generalized Walsh transf orm from a cube array specification of incompletely specified Boolean functions has been shown. The transforms algorithm makes use of the pr operties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. The computer impleme ntation drastically reduces the required time of computation by allowi ng calculation of only chosen coefficients in specified polarity. The entire spectrum-if required-can be computed incrementally for groups o f coefficients.