In-place and in-order algorithms for Paley- and sequency-orderedWalsh-Hadamard transforms

摘要

The in-place algorithms for the Hadamard-, Paley-, andsequency-ordered Walsh-Hadamard transform (WHT) are first reviewed. Allthese algorithms possess the FFT (fast Fourier transform) type butterflystructure. The in-place algorithms for the Paley- and sequency-orderedWHT require a pre- or post-bit reversal operation. By combining the bitreversal with the butterfly structure, in-place and in-order algorithmsfor the Paley- and sequency-ordered WHT are obtained. A FORTRANsubroutine for implementing both Paley- and sequency-ordered WHT islisted