Reciprocal Walsh Series

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-reciprocal1 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.