Section: New Results

Time-frequency transforms of white noises and Gaussian analytic functions

In signal processing, an important challenge is to be able to separate signals from ambient noises. In time-frequency analysis, this problem reduces to identify what is the spectrogram of a white noise to derive statistical tests in order to decide if some partial signal is noise or not. P. Fandrin recently put forward that the understanding of the zeros of the spectrograms would be already an important step by analyticity of the spectrograms. R. Bardenet and A. Hardy observed in [13] that there is a canonical way to identify the zeros of the usual white noise transforms associated to classical spectrograms and zeroes of Gaussian analytic functions associated with classical orthogonal polynomials in the background. In particular the zeros satisfy some invariance properties leading to computable correlation functions. In specific cases, one can identify some transforms whose zeros form a determinantal point process, in which case all the statistics of interests can be computed explicitly and this allows an exact numerical treatment.