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

• URL: http://arxiv.org/abs/2104.01293v1
• Date: Sat, 3 Apr 2021 02:19:07 GMT
• Title: Extraction of instantaneous frequencies and amplitudes in nonstationary time-series data
• Authors: Daniel E. Shea, Rajiv Giridharagopal, David S. Ginger, Steven L. Brunton, J. Nathan Kutz
• Abstract summary: We propose a data-driven approach to time-frequency analysis that circumvents many of the shortcomings of classic approaches. The method is demonstrated on a diversity of time-series data, including on data from cantilever-based electrostatic force microscopy.
• Score: 2.36991223784587
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 {\em nonstationary 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.

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