## 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 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

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

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.