Time–Frequency Filtering Based on Spectrogram Zeros

Abstract

For a proper choice of the analysis window, a short-time Fourier transform is known to be completely characterized by its zeros, which coincide with those of the associated spectrogram. A simplified representation of the time-frequency structure of a signal can therefore be given by the Delaunay triangulation attached to spectrogram zeros. In the case of multicomponent nonstationary signals embedded in white Gaussian noise, it turns out that each time–frequency domain attached to a given component can be viewed as the union of adjacent Delaunay triangles whose edge length is an outlier as compared to the distribution in noise-only regions. Identifying such domains offers a new way of disentangling the different components in the time–frequency plane, as well as of reconstructing the corresponding waveforms.