In this talk, we will bridge two research areas, namely the completeness problem for systems of translates in function spaces and the short-time Fourier transform (STFT) phase retrieval problem. As a first main result, we show that a complex-valued, compactly supported function can be uniquely recovered from samples of its spectrogram if certain density properties of an associated system of translates hold true. Secondly, we derive new completeness results for systems of discrete translates in spaces of continuous functions on compact sets. We finally combine these findings to deduce several novel recovery results from spectrogram samples. Our results hold for a large class of window functions, including Gaussians, all Hermite functions, as well as the practically highly relevant Airy disk function. Our results constitute the first recovery guarantees for the sampled STFT phase retrieval problem with a non-Gaussian window.   

This is joint work with P. Grohs and L. Liehr.

https://univienna.zoom.us/j/66031419470?pwd=bXd3V0xEMWM0MTQwS09nWStEV0NnUT09