The sine-type step waveform is an approximate reconstruction of a sine signal. Most existing research has neglected the characteristics of data in the transition region

especially the impact of Gibbs oscillations on the width of the plateau region

which has not yet received attention. The research on exploring the boundary of the transition region using mathematical models to obtain the plateau region is not deep enough. This paper analyzes the generation mechanism of Gibbs oscillations in sine-type step waveforms

establishes a digital representation method for Gibbs oscillations when truncating the Fourier series with finite terms

tracks the attenuation degree of the oscillation curve using amplitude envelope

constructs a quantitative mathematical expression for the plateau region of the step waveform based on mathematical models

and realizes “adaptive” point selection at both ends of the step waveform. The industrial frequency AC quantum standard electric energy meter developed based on the method proposed in this paper has a normalized error ranging from 0.2 to 0.4

improving the accuracy and stability of quantum measurement

thus providing new ideas for optimizing the operation of quantum voltage traceability.