Frequency Tracking with Spline Based Chirp Atoms

The tracking of prominent oscillations with time-varying frequencies is a common task in many signal processing applications. Therefore, efficient methods are needed to meet precision and run-time requirements. We propose two methods that extract the energy of the time frequency plane along a cubic spline trajectory. To raise efficiency, a sparse sampling method with dynamically shaped atoms is developed for the one method in contrast to standard Gabor atoms for the other. Numerical experiments using both synthetic and real-life data are carried out to show that dynamic atoms can significantly outperform classical Gabor formulations for this task.