Expansion of Walsh Functions in Terms of Shifted Rademacher Functions and Its Applications to the Signal Processing and the Radiation of Electromagnetic Walsh Waves

The expressions for Walsh functions in terms of shifted Rademacher functions are applicable to the design of a directive and selective array antenna for Walsh waves which is capable of eliminating the interference caused by impulsive noises. They also are applicable to voice processing because of their shift-invariant property. The shifted Rademacher functions were previously introduced by shiftiAg horizontally the periodic Rademacher functions. It was shown that the Walsh functions could be expressed as a linear combination of a finite number of the shifted Rademacher functions. This paper develops the actual expansions of the Walsh functions in terms of the shifted Rademacher functions. The coefficients in this series take only the values of either + 1 or -1. The shifted Rademacher coefficients appearing in the expansion of a given function in tenns of shifted Rademacher functions have the advantage that the coefficients of a shifted function are available by shifting cyclically the original coefficients.