"Finite-dimensional STFT phase retrieval for short windows"Bartusel, DavidWe study the phase retrieval problem associated with the finite-dimensional STFT, which tries to decide whether a finite-dimensional complex signal can be recovered (up to a global phase factor) from the modulus of its STFT with respect to a (finite-dimensional) window. It is well-known that this recovery is possible whenever the window's ambiguity function vanishes nowhere, and that this condition is met with probability 1 when the window is picked randomly. When considering a fixed window, many of the current results on this problem give sufficient conditions for non-vanishing signals or assume that the Fourier transform of the modulus squared of the window doesn't vanish. During the talk, we take a different approach by studying short windows and establish a unique characterization of phase retrieval for a large class of sparse signals. Checking these conditions turns out to be very convenient, since they only depend on the signal's support. |
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