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

Daniel E. Shea, Rajiv Giridharagopal, David S. Ginger, Steven L. Brunton, J. Nathan Kutz
2021 IEEE Access  
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. INDEX TERMS Signal analysis, parameter estimation, frequency estimation, amplitude estimation, spectral analysis, signal processing algorithms, machine learning.
doi:10.1109/access.2021.3087595 fatcat:mmx2vl56sjaj3do6jkfnoftxma