On the Walsh-Hadamard Transform and Prime Implicant Extraction

Abstract
The Walsh-Hadamard transform (WHT) provides a one-to-one mapping of n-variable Boolean functions onto an n-dimensional transform space. As such, it enables synthesis procedures to be carried out in the transform domain. This short paper discusses the role of the WHT in extracting prime implicants, which is pertinent to the overall minimization problem. First, a procedure to identify all the prime implicants of a 1-vertexl located at the origin is developed by inspecting the elements of a single inverse transform. Second, a theorem is proved to show how the signs of the transform coefficients can be changed, to obtain all the prime implicants of an arbitrazy 1-vertex via the same inverse transforn operation.

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