Functions consisting of a number of fixed-amplitude square pulses interposed with zeros. Following Harmuth (1969),
designate those with Even symmetry
and those with Odd symmetry
. Define the Sequency as half the number of zero crossings in the time base. Walsh functions with
nonidentical Sequencies are Orthogonal, as are the functions
and
. The product of two Walsh functions is also a Walsh function. The Walsh functions are then given by
See also Hadamard Matrix, Sequency
References
Beauchamp, K. G. Walsh Functions and Their Applications. London: Academic Press, 1975.
Harmuth, H. F. ``Applications of Walsh Functions in Communications.'' IEEE Spectrum 6, 82-91, 1969.
Thompson, A. R.; Moran, J. M.; and Swenson, G. W. Jr. Interferometry and Synthesis in Radio Astronomy.
New York: Wiley, p. 204, 1986.
Tzafestas, S. G. Walsh Functions in Signal and Systems Analysis and Design. New York: Van Nostrand Reinhold, 1985.
Walsh, J. L. ``A Closed Set of Normal Orthogonal Functions.'' Amer. J. Math. 45, 5-24, 1923.