Signal Analysis via the Stochastic Geometry of Spectrogram Level Sets

Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. maxima. This is complemented by a recent interest zeros or minima, following seminal work Flandrin and others, which exploits connections with Gaussian analytic functions (GAFs). However, zero sets (or extrema) GAFs have complicated stochastic structure, complicating any direct theoretical analysis. Standard techniques largely rely on statistical observables from spatial data, whose distributional properties for mostly understood only at an empirical level. In this work, we investigate spectrogram examination geometric level sets. We obtain rigorous theorems demonstrating efficacy based approach to detection estimation signals, framed concrete inferential set-up. Exploiting these ideas as underpinnings, propose algorithm signal that intrinsic given substantiate its effectiveness extensive studies. Our results also implications approaches To our knowledge, arguably among first provide understanding reconstruction set up, provable guarantees thresholds rates convergence.