This thesis describes a proposed design of a special-purpose digital instrument that will obtain the first 32 coefficients of the Walsh-Fourier series of a low-fundamental frequency periodic voltage. The mathematics are developed for applying Walsh functions to obtain a Walsh-Fourier series in the same manner as sinusoidal waves are used to obtain a Fourier series of a periodic wave. It is shown how Walsh-Fourier coefficients are employed to obtain a Fourier series. Some familiar waveforms are shown as examples. The mathematical concepts are applied to the design of the instrument, of which two major portions have been constructed using integrated circuits. The Walsh-Fourier coefficients are available at the end of the second cycle of the input. The upper fundamental frequency limit of the instrument is approximately 60 Hz. There is no low-frequency limit.