Unified algorithm to generate Walsh functions in four different orderings and its programmable hardware implementations

The paper presents an algorithm to generate Walsh functions in four different orderings: Hadamard, Harmuth, Paley and strict sequencing. By the analysis of the properties and mutual relations among these four orderings, the authors found a unified approach to generate any of the orderings from the primary set of Rademacher functions. By using these properties, the authors developed a programmable Walsh function generator for 64 outputs by both field programmable gate arrays and lookup table 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.