Programmable Hardware Implementation Based on Four Walsh Sequences

This article shows an algorithm to generate Walsh functions in four different orderings: Hadamard, Harmuth, Paley and strict sequency. The properties and mutual relations among these four orderings are analyzed and a method is developed that allows any of the orderings to be generated from the primary set of Rademacher functions. Finally, a programmable Walsh function generator for 64 outputs is implemented using both field programmable gate arrays (FPGAs) and lookup table (LUT) cascades to estimate the amount of hardware and performance. Such a programmable Walsh function generator can be used in VLSI testing, CDMA, pattern recognition as well as image and signal processing.