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

TL;DR

This paper introduces a data-driven method called nonstationary Fourier mode decomposition (NFMD) that accurately extracts instantaneous frequencies and amplitudes from nonstationary, nonlinear time-series data, overcoming limitations of traditional techniques.

Contribution

The paper presents NFMD, a novel approach combining modern algorithms for improved time-frequency analysis of complex nonstationary signals.

Findings

Successfully applied to nanoscale electrostatic force microscopy data.

Outperforms classic methods in handling nonstationary signals with discontinuities.

Provides precise identification of instantaneous frequencies and amplitudes.

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.