An Artificial Intelligence-Assisted Adaptive Complexing Algorithm for Robust RMS Estimation of Harmonic Signals from Short Data Records

Abstract

Windowed spectral (DFT-based) estimation of the root-mean-square (RMS) value of a harmonic signal is widely reported to suppress the systematic error caused by non-coherent (fractional-period) sampling that afflicts classical time-domain RMS estimators. This paper reports a previously undocumented limitation of that claim: for short data records (e.g., N = 32 samples) and signal-to-sampling-frequency ratios Fc/fd close to the analysis band edges (near 0 or 0.5), a windowed-DFT estimator can be markedly less accurate than the plain time-domain estimator it is meant to improve upon, because the window's main-lobe width, relative to the small number of available spectral bins, forces the summation band used for the RMS recovery to overlap the DC or Nyquist edge, where the positive/negative-frequency energy-split assumption underlying essentially all windowed-DFT RMS estimators breaks down. We formalize this failure mode, propose a lightweight, ground-truth-free detection statistic based on the distance (in spectral bins) between the dominant peak and the nearest spectrum edge, and use it to drive a simple adaptive switching ("complexing") rule between the time-domain and windowed-DFT estimators. Across a full Fc/fd sweep, 36 initial phases, and N in {32, 64, 128, 256}, the proposed switched estimator's worst-case relative error is shown, by direct simulation, to never exceed the better of the two individual methods for any tested N, closing the gap identified above while preserving the large accuracy gains of windowed-DFT estimation away from the band edges. MATLAB implementation (R2016a-compatible) is provided.