The time evolution of the frequency content of a real variable function is often investigated by means of a two-dimensional representation known as the short-time Fourier transform (STFT). The zero set of the STFT encodes rich information and exhibits a rather rigid pattern as soon as the analyzed signal is impacted by even a moderate amount of noise. In fact, in many important cases, the theory of gaussian analytic functions can be brought to bear to provide refined statistics for such zero sets.

I will present recent results on statistics of zero sets of STFTs of random signals, and on the performance of algorithms for their computation from finite data. Joint work with Luis Alberto Escudero, Naomi Feldheim, Antti Haimi and Guenther Koliander.