Family of generalised multi-polarity complex Hadamard transforms

A family of generalised complex Hadamard transforms using the concept of po larity is introduced. Forward and inverse transformation kernels and method s of recursive generation of transform matrices using Kronecker products of elementary matrices are shown. Mutual relationships among transform matric es and spectra for arbitrary polarities are presented. Efficient ways of ca lculating spectra for logic functions through decision diagrams are also sh own. The half-spectrum property is used to reduce further the computational requirements for both fast transforms and decision diagram based calculati ons.