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Planar Sampling Sets for the Short-Time Fourier Transform

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Abstract

This paper considers the problem of restricting the short-time Fourier transform to sets of nonzero measure in the plane. Thereby, we study under which conditions one has a sampling set and provide estimates of the corresponding sampling bound. In particular, we give a quantitative estimate for the lower sampling bound in the case of Hermite windows and derive a sufficient condition for a large class of windows in terms of a certain planar density. On the way, we prove a Remez-type inequality for polyanalytic functions.

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Acknowledgements

M. Speckbacher was supported by an Erwin–Schrödinger Fellowship (J-4254) of the Austrian Science Fund FWF. The authors are grateful to the anonymous referees for their constructive remarks that lead to an improvement of the presentation of our results.

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Authors and Affiliations

  1. Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, 33400, Talence, France

    Philippe Jaming & Michael Speckbacher

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  1. Philippe Jaming
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  2. Michael Speckbacher
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Correspondence to Philippe Jaming.

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Communicated by Kristian Seip.

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Jaming, P., Speckbacher, M. Planar Sampling Sets for the Short-Time Fourier Transform. Constr Approx 53, 479–502 (2021). https://doi.org/10.1007/s00365-020-09503-4

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  • DOI: https://doi.org/10.1007/s00365-020-09503-4

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