On spectrogram local maxima

Abstract

In close connection with time-frequency uncertainty relations, spectrograms are known to have some built-in redundancy which constrains the landscape of their surface, thus calling for simplified descriptions based on a reduced number of salient features. This is investigated here in some detail for spectrogram local maxima in the generic case of white Gaussian noise. A simple model, based on a randomized hexagonal lattice structure, is proposed for the distribution of their time-frequency locations considered as realizations of a 2D point process in the plane. While the rationale of the model is discussed and its relevance tested, further consideration is also given to the distribution of maximal values as well as to that of zeros that can be inferred from the proposed model.