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 adaptive minimal grid neighbors 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 \(\delta \), AMN is shown to compute the desired zero set up to a factor of \(\delta \) in the Wasserstein error metric, with failure probability \(O(\delta ^4 \log ^2(1/\delta ))\). We also provide numerical tests and comparison with other algorithms.

我们研究了被复杂白噪声污染的信号的 Bargmann 变换的零集的计算，或者等效地，使用高斯窗计算其短时傅里叶变换的零点。我们介绍了自适应最小网格邻居算法 (AMN)，这是最近出现在信号处理文献中的一种方法的变体，并证明它以高概率计算所需的零集。更准确地说，给定具有间距\(\delta \)的有限网格上的信号的 Bargmann 变换样本，AMN 被显示为计算所需的零，设置为Wasserstein 误差度量中的因子\(\delta \) , 失败概率\(O(\delta ^4 \log ^2(1/\delta ))\). 我们还提供数值测试和与其他算法的比较。