Recurrent neural network topologies for spectral state estimation and differentiation

This paper presents three recurrent neural networks to estimate the spectral content of (noisy) periodic waveforms that are common in many engineering processes. The presented (structured) networks, 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 proposed networks perform differentiation in the frequency domain and thus are immune to uncorrelated measurement noise. Furthermore, due to the moving-average based correlation scheme, which is inherent to the recursive transform, the presented networks can handle composite waveforms without a detailed signal model in the frequency domain. The performance of the proposed network architectures in a number of simulation and experimental cases has also been evaluated in this paper.