Efficient Computation of the Zeros of the Bargmann Transform Under Additive White Noise.

We study the computation of the zero set of the Bargmann transform of a signal contaminated with complex white noise, or, equivalently, the computation of the zeros of its short-time Fourier transform with Gaussian window. We introduce the algorithm (AMN), a variant of a method that has recently appeared in the signal processing literature, and prove that with high probability it computes the desired zero set. More precisely, given samples of the Bargmann transform of a signal on a finite grid with spacing , AMN is shown to compute the desired zero set up to a factor of in the Wasserstein error metric, with failure probability .

An asymptotic formula for the variance of the number of zeroes of a stationary Gaussian process.

We study the variance of the number of zeroes of a stationary Gaussian process on a long interval. We give a simple asymptotic description under mild mixing conditions. This allows us to characterise minimal and maximal growth.