A family of generalised complex Hadamard transforms using the concept of polarity is introduced. Forward and inverse transformation kernels and methods of recursive generation of transform matrices using Kronecker products of elementary matrices are shown. Mutual relationships among transform matrices and spectra for arbitrary polarities are presented. Efficient ways of calculating spectra for logic functions through decision diagrams are also shown. The half-spectrum property is used to reduce further the computational requirements for both fast transforms and decision diagram based calculations.
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