Walsh Function
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 withnonidentical 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
The Walsh functions Cal(
) for 
, 1, ..., 
and for 
, 2, ..., 
are given by therows of the Hadamard Matrix 
.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.
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