标题： 一种求解噪声复指数逼近问题的新变换方法 显示英文标题

标题： A new transform for solving the noisy complex exponentials approximation problem

摘要： 考虑了从有限数量的受加性独立同分布高斯噪声影响的复矩出发，估计由复平面上点为中心的狄拉克分布线性组合构成的复测度的问题。定义了一个随机测度，在适当条件下其期望近似未知测度。随后提出了一种逼近测度的估计器以及一种新的离散变换，该变换可以用于计算未知测度的估计值。还进行了一项小型模拟研究，以实验验证这些近似的有效性。 显示英文摘要

摘要： The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered. A random measure is defined whose expectation approximates the unknown measure under suitable conditions. An estimator of the approximating measure is then proposed as well as a new discrete transform of the noisy moments that allows to compute an estimate of the unknown measure. A small simulation study is also performed to experimentally check the goodness of the approximations.