Time-Frequency Analysis of Non-Uniformly Sampled Signals via Sample Density Adaptation

The analysis of non-stationary signals in non-uniformly sampled data is a challenging task. Time-integrated methods, such as the generalised Lomb-Scargle (GLS) periodogram, provide a robust statistical assessment of persistent periodicities but are insensitive to transient events. Conversely, existing time-frequency methods often rely on fixed-duration windows or interpolation, which can be suboptimal for non-uniform data. We introduce the non-uniform Stockwell-transform (NUST), a time-frequency framework that applies a localized density adaptive spectral analysis directly to non-uniformly sampled data. NUST employs a doubly adaptive window that adjusts its width based on both frequency and local data density, providing detailed time-frequency information for both transient and persistent signals. We validate the NUST on numerous non-uniformly sampled synthetic signals, demonstrating its superior time-localization performance compared to GLS. Furthermore, we apply NUST to HARPS radial velocity data of the multi-planetary system HD 10180, successfully distinguishing coherent planetary signals from stellar activity.

💡 Research Summary

The paper introduces the Non‑Uniform Stockwell Transform (NUST), a novel time‑frequency analysis framework designed to operate directly on irregularly sampled data without the need for interpolation. Traditional approaches fall into two categories: time‑integrated methods such as the Generalised Lomb‑Scargle (GLS) periodogram, which provide robust global spectral estimates but lack temporal resolution, and time‑frequency methods like the Short‑Time Fourier Transform (STFT) or the classic Stockwell Transform, which assume uniformly spaced samples and therefore require resampling that can introduce artefacts.

NUST bridges this gap by embedding a localized GLS fit within a doubly adaptive Gaussian window. The window’s standard deviation is defined as

σ_adaptive(τ,f) = α · |f|⁻¹ ·