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Statistical properties of signals approximated by orthogonal polynomials and Schur parametrization

机译:正交多项式和Schur参数化近似信号的统计性质

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In the paper, we investigate reconstruction of statistical properties of signals approximated in various orthogonal bases. The approximation of signals is performed in various polynomial bases and by Schur parametrization algorithm. To compare quality of remodeled signals in different bases, we use mean square error criterion for power spectral density. The correlation function, and the derived from it power spectral density, is sufficient to describe signal statistical properties. The numerical experiments were performed using benchmark signals. The tests were executed for different polynomial degrees and different orders of Schur innovation filtering. Our purpose was to find which patrametrization method requires less parameters.
机译:在本文中,我们研究了在各种正交基中近似的信号统计特性的重建。信号的逼近以各种多项式为基础,并通过Schur参数化算法进行。为了比较不同基准中重塑信号的质量,我们对功率谱密度使用均方误差准则。相关函数以及从中得出的功率谱密度足以描述信号统计特性。使用基准信号进行了数值实验。针对不同的多项式次数和不同阶数的Schur创新滤波执行测试。我们的目的是找到哪种参数化方法需要较少的参数。

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