Fast multi-polarity complex Hadamard transform for logic functions

Abstract

A new formulation of Fast Multi-Polarity Complex Hadamard Transform has been introduced. Forward and inverse transformation kernels and the ways of recursive generation of transform matrices by using Kronecker products of elementary matrices have been given. Mutual relations among transform matrices and spectra for arbitrary polarities have been presented. Efficient ways of calculating spectra for logic functions through decision diagrams are also shown. Half-spectrum property is used to reduce the computational requirements for both fast transforms and decision diagrams based calculations.