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

The in-place algorithms for the Hadamard-, Paley-, and sequency-ordered Walsh-Hadamard transform (WHT) are first reviewed. All these algorithms possess the FFT (fast Fourier transform) type butterfly structure. The in-place algorithms for the Paley- and sequency-ordered WHT require a pre- or post-bit reversal operation. By combining the bit reversal with the butterfly structure, in-place and in-order algorithms for the Paley- and sequency-ordered WHT are obtained. A FORTRAN subroutine for implementing both Paley- and sequency-ordered WHT is listed.<<ETX>>