Sampling trajectories for the short-time Fourier transform

2021/06/02 by Speckbacher, Michael
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2106.01018

Abstract

We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in \R². We first consider 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.

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