Digital Walsh-Fourier Analysis of Periodic Waveforms

Abstract

A digital process is described for obtaining the Walsh-Fourier series of a periodic waveform, which requires at most two cycles of the waveform under measurement. The first cycle of the periodic waveform is required for the determination of period. The coefficients of the Walsh-Fourier series are obtained during the second cycle only, and they are available at the end of the cycle. Given the Walsh-Fourier coefficients of the periodic wave, the individual sine and cosine components of its Fourier series may be obtained using conversion formulas. Special features of the process are that there are no theoretical low-frequency limitations, and for an instrument with an internal clock whose frequency lies in the range 1 Hz to 1 MHz, the fundamental frequency component of a signal that can be analyzed would be in the range 1 cycle in 11.6 days to 60 Hz. Also, whereas the digital processes required to obtain a Fourier series directly are complicated by the need to multiply sample values of voltage by sines and cosines, which are themselves functions of time, determination of Walsh-Fourier coefficients is achieved very simply by using gating circuits. Generation of the required Walsh functions for a periodic signal of any fundamental frequency within the design range has been achieved.