Paley, Hadamard, and Walsh Functions: Interrelationships and Transconversions.
SYRACUSE UNIV N Y DEPT OF ELECTRICAL AND COMPUTER ENGINEERING
Pagination or Media Count:
Paley, Hadamard, and Walsh functions are binary-valued functions which form a complete orthonormal set on the interval 0 or xc1. All of them have been referred to as Walsh functions in the literature, leading to considerable confusion in nomenclature. This report defines and differentiates Paley, Hadamard, and Walsh functions from their expressions as products of Rademacher functions. Their interrelationships and the procedures for converting one function to another are discussed. Methods for determining the sequency from the order of a Paley function and of a Hadamard function are explained. An algorithm providing a simple way for obtaining the sequency vector of high-order Hadamard transform matrices is developed.
- Theoretical Mathematics