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.

© 1996-9

1999-05-26