A consideration of orthogonal matrices, other than the Rademacher-Walsh types, for the synthesis of digital networks
A.M. Lloyd · International Journal of Electronics · 1979
By correlating the output vector of a logic circuit to the functions represented in the rows of the Rademacher-Walsh matrix, it has been shown that synthesis is possible by establishing the similarity of the circuit to particular standard functions (Lechner 1971, Karpovsky 1976. Edwards 1975, Hurst 1973). However this specific matrix has the limitation that the only functions embedded within it are the independent, xi input variables, and the exclusive-OR relationships between them. Thus a circuit which employs, say, only one AND gate cannot be synthesized directly from the correlation coefficients produced by the Rademacher-Walsh transform, although it may lie possible using other transforms. This paper discusses the existence of other orthogonal matrices, whose elements remain either + 1 or − 1, and shows how they are linked together under simple constraints