Composite complex Hadamard spectra of Boolean functions

A new class of orthogonal transform, Complex Hadamard Transform is proposed as a spectral technique for analysis, synthesis and testing of Boolean functions. The method is presented to evaluate Complex Hadamard Spectra of AND, OR and XOR of Boolean functions directly front the spectra of the separate Boolean functions. The results are given using a general coding scheme, and different possible coding of Boolean functions are discussed. Moreover, new definition of the convolution operation called complex convolution is derived. Different properties of such a convolution are presented. Theorem giving final formulae for composite complex Hadamard spectra of Boolean functions is stated in terms of complex convolution. By using presented methods, many of the Boolean operations in original domain can be represented much simpler in terms of their composite complex spectra