Extraction of instantaneous frequencies and amplitudes in nonstationary time-series data
This method addresses the challenge of analyzing nonstationary signals in science and engineering, offering a data-driven approach to improve time-frequency analysis.
The authors tackled the problem of extracting instantaneous frequencies and amplitudes from nonstationary time-series data with discontinuities, proposing a nonstationary Fourier mode decomposition method that accurately identifies these components, as demonstrated on data like cantilever-based electrostatic force microscopy.
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.