Reciprocal Walsh Series

Abstract-Any basis function of a generalized Fourier series takes on many values in an interval. In contrast, the binary nature of the basis functions of Walsh-Fourier series (WFS) allows them to be considered self-reciprocall except for a finite number of discontinuities. Hence, quotients of linear combinations of Walsh functions may be used to generate series representations of reciprocals of periodic functions. Thus the usual summation techniques employed to evaluate series representations of nonsquare-integrable periodic functions may, in some instances, be circumvented. An algorithm is discussed which uses the WFS coefficients for a given periodic function to estimate the WFS coefficients for the corresponding reciprocal function. Selected reciprocals of finite series and approximations to reciprocals of infinite series illustrate the algorithm.