Sampling Trajectories for the Short-Time Fourier Transform

We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $$ . We first investigate the interplay between relative density of the trajectory and the reconstruction property. Later, we consider spiraling curves, a special class of trajectories, and connect sampling and uniqueness properties of these sets. Moreover, we show that for window functions given by a linear combination of Hermite functions, it is indeed possible to stably reconstruct from samples on some particular natural choices of spiraling curves.