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

arXiv: https://arxiv.org/abs/2104.01293 · HTML: https://mlsanity.com/paper/2104.01293/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 56 references that are in the map.
- First posted on arXiv 3 Apr 2021.

## Builds on (most cited first, 5 of 5)

- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Multivariate Variational Mode Decomposition](https://mlsanity.com/paper/1907.04509/) (2019)
- [The Fourier Decomposition Method for nonlinear and nonstationary time series analysis](https://mlsanity.com/paper/1503.06675/) (2015)
- [Data-driven Spatiotemporal Modal Decomposition for Time Frequency Analysis](https://mlsanity.com/paper/1806.08739/) (2018)
- [Convex Optimization approach to signals with fast varying instantaneous frequency](https://mlsanity.com/paper/1503.07591/) (2015)

## Built on by (most cited first, 3 of 3)

- [Active Learning of Quantum System Hamiltonians yields Query Advantage](https://mlsanity.com/paper/2112.14553/) (2021)
- [Adaptive Latent Space Tuning for Non-Stationary Distributions](https://mlsanity.com/paper/2105.03584/) (2021)
- [Adaptive conditional latent diffusion maps beam loss to 2D phase space projections](https://mlsanity.com/paper/2502.18684/) (2025)

## Abstract (arXiv)

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.