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

Abstract

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.