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Sampling at twice the Nyquist rate in two frequency bins guarantees uniqueness in Gabor phase retrieval

by M. Wellershoff

(Report number 2022-30)

Abstract
We demonstrate that a fourfold redundancy in the measurements is sufficient for uniqueness in sampled Gabor phase retrieval with bandlimited signals and thereby draw a parallel between the sampled Gabor phase retrieval problem and finite-dimensional phase retrieval problems. Precisely, we show that sampling at twice the Nyquist rate in two frequency bins guarantees uniqueness in Gabor phase retrieval for signals in the Paley-Wiener space.

Keywords: 94A12, 42B10

@Techreport{W22_1018,
  author = {M. Wellershoff},
  title = {Sampling at twice the Nyquist rate in two frequency bins guarantees uniqueness in Gabor phase retrieval},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-30},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-30.pdf },
  year = {2022}
}

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