An industrially useful means for decomposition and differentiation of harmonic components of periodic waveforms

This paper presents efficient methods to estimate the spectral content of (noisy) periodic waveforms that are common in industrial processes. The techniques presented, which are based on the recursive discrete Fourier transform, are especially useful in computing high-order derivatives of such waveforms. Unlike conventional differentiating techniques, the methods presented differentiate in the frequency domain and thus are quite immune to uncorrelated measurement noise. This paper also shows the theoretical relationship between the proposed methods and those of well-known resonant filters.