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

DOI10.1007/S00041-022-09990-YOpenAlexW4313204164MaRDI QIDQ2686571

Matthias Wellershoff

Publication date: 28 February 2023

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.03946

zbMATH Keywords

Gabor transformphase retrievalHadamard factorisation theoremMüntz-Szász type resultNyquist-Shannon sampling

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Sampling theory in information and communication theory (94A20)

Related Items (2)

Non-Uniqueness Theory in Sampled STFT Phase Retrieval ⋮ Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions

Cites Work

• Foundations of time-frequency analysis
• Phase retrieval and magnitude retrieval of entire functions
• Quantum tomography under prior information
• Phase retrieval from sampled Gabor transform magnitudes: counterexamples
• Injectivity of Gabor phase retrieval from lattice measurements
• On signal reconstruction without phase
• Uniqueness of STFT phase retrieval for bandlimited functions
• On a Hilbert space of analytic functions and an associated integral transform part I
• On Approximation by Shifts and a Theorem of Wiener

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