Extraction of instantaneous frequencies and amplitudes in nonstationary time-series data [article]

Daniel E. Shea, Rajiv Giridharagopal, David S. Ginger, Steven L. Brunton, J. Nathan Kutz
2021 arXiv   pre-print
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral analysis, we propose a data-driven approach to time-frequency analysis that circumvents many of the shortcomings of classic approaches, including the extraction of nonstationary signals with discontinuities in their behavior. The method introduced is equivalent to a
more » ... onstationary Fourier mode decomposition (NFMD) for nonstationary and nonlinear temporal signals, allowing for the accurate identification of instantaneous frequencies and their amplitudes. The method is demonstrated on a diversity of time-series data, including on data from cantilever-based electrostatic force microscopy to quantify the time-dependent evolution of charging dynamics at the nanoscale.
arXiv:2104.01293v1 fatcat:yehomdsynrdgznuexyibdgyjea