Flat-cylinder sampling/interpolation versus Paley–Wiener completeness in STFT phase retrieval for bandlimited signals

Investigate whether the sampling and interpolation theorems on the flat cylinder C/Z—together with the associated uniqueness sets for Fock-type spaces—can replace the completeness results for exponential systems and Paley–Wiener spaces in proving uniqueness of STFT phase retrieval for bandlimited functions, as in Grohs–Liehr (Appl. Comput. Harmon. Anal., 2023).

Background

The paper suggests a variant of the theory in which periodicity is imposed in frequency to analyze bandlimited functions, naturally leading to a flat cylinder phase space. Uniqueness in STFT phase retrieval for bandlimited signals has recently been studied by Grohs–Liehr, relying on completeness of exponential systems and Paley–Wiener spaces.

The authors pose whether their sampling/interpolation results and implied uniqueness sets for Fock-type spaces on the flat cylinder could serve as an alternative foundation to establish such uniqueness, potentially yielding new proofs or generalizations of STFT phase retrieval results for bandlimited signals.