An algorithm to compute the sequency ordered Walsh transform

Abstract

A fast sequency-ordered Walsh transform algorithm is presented; this sequency-ordered fast transform is complementary to the sequency-ordered fast Walsh transform introduced by Manz (1972) and eliminating gray code reordering through a modification of the basic fast Hadamard transform structure. The new algorithm retains the advantages of its complement (it is in place and is its own inverse), while differing in having a decimation-in time structure, accepting data in normal order, and returning the coefficients in bit-reversed sequency order. Applications include estimation of Walsh power spectra for a random process, sequency filtering and computing logical autocorrelations, and selective bit reversing.