Generation of Gray code ordered Walsh functions by symmetric and shift copies

A new theoretical formulation of Gray code ordered Walsh functions by symmetric and shift copies is presented. The formulation is based on different operations on matrices together with some symmetry features of Gray code ordered Walsh functions. The method by which the Walsh functions are ordered is determined mainly by convenience. Walsh transforms in Gray code order are advantageous over other ordering when the generation of each separate Walsh spectral coefficient is implemented in hardware. The layout for VLSI implementation of such a generator has the minimal number of crossings and occupies a smaller chip area than for other orderings of Walsh functions