  In a recent paper, Flandrin [2015] has proposed filtering based on the zeros
of a spectrogram, using the short-time Fourier transform and a Gaussian window.
His results are based on empirical observations on the distribution of the
zeros of the spectrogram of white Gaussian noise. These zeros tend to be
uniformly spread over the time-frequency plane, and not to clutter. Our
contributions are threefold: we rigorously define the zeros of the spectrogram
of continuous white Gaussian noise, we explicitly characterize their
statistical distribution, and we investigate the computational and statistical
underpinnings of the practical implementation of signal detection based on the
statistics of spectrogram zeros. In particular, we stress that the zeros of
spectrograms of white Gaussian noise correspond to zeros of Gaussian analytic
functions, a topic of recent independent mathematical interest [Hough et al.,
2009].

Methodology