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首页> 外文会议>International Conference on Renewable Energies for Developing Countries >Second Order Statistics of the Scattering Vector Defining the D-T Nonlinear Fourier Transform
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Second Order Statistics of the Scattering Vector Defining the D-T Nonlinear Fourier Transform

机译：定义D-T非线性傅里叶变换的散射矢量的二阶统计量

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The impact of time-domain noise on the nonlinear Fourier transform is currently not well understood. Most, if not all, available results are based on perturbation theory and become exact only in the low-noise regime. In this paper, it is pointed out that the mean and the (conventional and complementary) covariance of the scattering vector [a(z) b(z)](exp T) that is used to define the discrete-time nonlinear Fourier transform can be computed exactly if a known deterministic signal is contaminated with circular symmetric white noise. Since the scattering vector is a polynomial in z(exp -1), also the second-order statistics of its coefficient vector are derived. This result is finally used to determine the second-order statistics of an arbitrary multipoint scattering vector, in which the values of the scattering vector for several arguments are stacked. The results are illustrated in a numerical example, and potential extensions are discussed.
机译：时域噪声对非线性傅里叶变换的影响目前尚不十分清楚。大部分（如果不是全部）可用的结果都是基于微扰理论，并且仅在低噪声状态下才变得精确。本文指出，用于定义离散时间非线性傅里叶变换的散射矢量[a（z）b（z）]（exp T）的均值和（常规和互补）协方差可以如果已知的确定性信号被圆形对称白噪声污染，则可以精确计算。由于散射矢量是z（exp -1）的多项式，因此还导出了其系数矢量的二阶统计量。该结果最终用于确定任意多点散射向量的二阶统计量，其中堆叠了多个自变量的散射向量的值。结果在一个数值示例中进行了说明，并讨论了潜在的扩展。

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