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The optimum estimation of statistical signals based on systematic expression of many types of sample arrays in multidimensional space

机译:基于多维空间中多种样本阵列系统表达的统计信号最优估计

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Extended interpolatory approximation is discussed for some classes of n-dimensional statistical signals. Firstly, we present two sufficient conditions of the optimum approximation. Then, as example of this optimum approximation, we consider approximation of n-dimensional statistical signals expressed by linear combination of the finite set of base signals in a n-dimensional space. We assume that these signals have generalized mutual moment smaller than a given positive number. Related topic was discussed. However, discrete running approximation along the time axis that uses shift-invariant interpolation functions with the finite supports is not treated. In the final part of this paper, we discuss best running approximation of n-dimensional signals expressed by linear combination of the finite set of sinusoidal signals in a n-dimensional space. The presented methods have the minimum measure of approximation error among all the linear and the nonlinear approximations using the same measure of error and generalized sample values.
机译:对于某些类别的n维统计信号,讨论了扩展的内插近似。首先,我们给出了最佳逼近的两个充分条件。然后,作为该最佳逼近的示例,我们考虑由n维空间中基本信号的有限集合的线性组合表示的n维统计信号的逼近。我们假设这些信号的广义互矩小于给定的正数。讨论了相关主题。但是,未处理在时间轴上使用带有有限支撑的不变位移插值函数的离散运行近似。在本文的最后部分,我们讨论了由n维空间中正弦信号有限集的线性组合表示的n维信号的最佳运行逼近。所提出的方法使用相同的误差和广义样本值,在所有线性和非线性近似中具有最小的近似误差。

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