Sparse Off-the-Grid Computation of the Zeros of STFT

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Abstract
The Short Time Fourier Transform (STFT) of white noise presentwell-knownproperties regarding the distribution of its zeroes. In this letter, we propose a method to locate them beyond the usual time-frequency grid, in order to gain a better understanding on the underlying point process. To do so, we use a recent method based on off-the-grid sparse analysis, that aim at finding the best set of atomic shape forming the STFT modulus. We also improve it by ensuring the resulting combination of atoms minimizes a criterion based on the theoretical behavior of the set of zeros. Numerical experiments support our approach and show, with respect to discrete methods, an improved statistical power for the detection of signals in white noise.

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