1. Extraction of Instantaneous Frequencies and Amplitudes in Nonstationary Time-Series Data
- Author
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Daniel E. Shea, Rajiv Giridharagopal, David S. Ginger, Steven L. Brunton, and J. Nathan Kutz
- Subjects
Signal analysis ,parameter estimation ,frequency estimation ,amplitude estimation ,spectral analysis ,signal processing algorithms ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - 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 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.
- Published
- 2021
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