{
  "id": "2106.01018",
  "version": "v1",
  "published": "2021-06-02T08:34:18.000Z",
  "updated": "2021-06-02T08:34:18.000Z",
  "title": "Sampling trajectories for the short-time Fourier transform",
  "authors": [
    "Michael Speckbacher"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $\\R^2$. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-02T08:34:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short-time fourier transform",
      "sampling trajectories",
      "trajectory",
      "spiraling curves",
      "natural choices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}