Ashwini Kulkarni supervised by Dr. Santosh Nannuru received her Master of Science – Dual Degree in Electronics and Communication Engineering (LED) by Research. Here’s a summary of her research work on Signal Processing Methods for Exoplanet Detection via Radial Velocity Measurements
The detection of exoplanets using the radial velocity (RV) method is fundamentally a signal processing challenge. Planetary signals are small sub-meter-per-second Doppler shifts embedded in time series corrupted by stellar variability, instrumental systematics, and the irregular observational schedules inherent to ground-based astronomy. This thesis addresses this challenge from two directions: a comprehensive review of existing methods, and the development of a new time-frequency analysis framework—the Non-Uniform Stockwell Transform (NUST), specifically designed for the non-uniformly sampled, non-stationary signals encountered in precision RV surveys.
The first contribution is a systematic review of fifteen signal processing methods used for RV exoplanet detection, ranging from the Lomb-Scargle periodogram and its Bayesian extensions, through Gaussian process regression, Bayesian MCMC inference, wavelet-based approaches, and machine learning classifiers. Each method is analysed in terms of its mathematical foundations, handling of non-uniform sampling and correlated noise, computational cost, and limitations. A comparative summary table provides a practical reference for method selection.
The second and central contribution is the theoretical development and experimental validation of the NUST. The NUST extends the Stockwell transform, a time-frequency representation providing frequency-dependent time resolution through a Gaussian analysis window, to handle non-uniformly sampled data without interpolation. Its core innovation is a doubly adaptive Gaussian window whose width scales with both the analysis frequency and the local sample density at each point in time, ensuring statistically consistent resolution across densely and sparsely observed periods. At each time-frequency point a localised Generalised Lomb-Scargle fit is performed, connecting the NUST directly to the standard GLS significance framework and producing a real-valued power statistic bounded between zero and one. The method is validated on synthetic datasets with injected planetary signals and on archival data from the multiplanetary systems HD 10180, HD 40307, and GJ 581, where it separates the temporally coherent power of confirmed planetary signals from the evolving, season-dependent signature of stellar activity, a diagnostic capability that the GLS periodogram, operating in the frequency domain alone, cannot provide.
Current limitations include the absence of an analytical global significance threshold, manual hyperparameter tuning, and an assumption of uncorrelated noise within each window. Extensions proposed include a Keplerian NUST for eccentric-orbit detection, integration with Bayesian pipelines, and a multi-dimensional variant for joint analysis of RV and stellar activity indicators. The broader applicability of the NUST to other non-uniformly sampled, non-stationary domains, variable star photometry, paleoclimate proxy analysis, long-term biomedical monitoring, and structural health monitoring is also discussed.
July 2026