CLASSIFICATIONS AND GRAPH-BASED REPRESENTATIONS OF SWITCHING-FUNCTIONS USING A NOVEL COMPLEX SPECTRAL TECHNIQUE

In this paper, a novel spectral technique based on the transform const ructed from a Complex Hadamard matrix is introduced. The technique fin ds potential applications in various synthesis and optimization proces ses of logic circuits. Classification of switching function is shown h ere as one of the possible applications. The technique uses the Comple x Hadamard matrix as the spectral transform, manipulates the complex s pectral coefficients of the functions and classifies them into the NPN -equivalent and linearly separable functions. The method has proven to be a more efficient classification scheme than the existing classific ation method using the standard spectral technique based on the Walsh Transform. For efficient manipulation of switching functions, some new decision diagrams to represent Complex Hadamard matrices and their sp ectra of integer-valued functions are proposed. With the intrinsic pro perties of the new transform in handling complex numbers, the presente d decision diagrams lead to a more efficient and compact representatio n of both switching and complex functions.