Metrics for Power Spectra: An Axiomatic Approach
Metrics for Power Spectra: An Axiomatic Approach
复制标题
功率谱的度量：公理化方法
DOI：
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发表时间：
2009
影响因子：
5.4
通讯作者：
M. S. Takyar
中科院分区：
文献类型：
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作者：
T. Georgiou;J. Karlsson;M. S. Takyar
我们提出了一个公理化的框架，寻求功率谱密度函数之间的距离。这些公理要求所寻求的度量尊重加性和乘性噪声在降低我们辨别光谱的能力方面的影响，以及它们要求关于度量中测量的扰动的统计量的连续性。然后，我们提出了一个特定的度量，遵守这些要求。该度量是基于蒙格-康托洛维奇运输问题，并与早期的黎曼度量的基础上的最小方差预测几何的基本时间序列。它也被比较与更传统的Itakura-Saito距离测量，以及上述预测指标，在两个代表性的例子。
We present an axiomatic framework for seeking distances between power spectral density functions. The axioms require that the sought metric respects the effects of additive and multiplicative noise in reducing our ability to discriminate spectra, as well as they require continuity of statistical quantities with respect to perturbations measured in the metric. We then present a particular metric which abides by these requirements. The metric is based on the Monge-Kantorovich transportation problem and is contrasted with an earlier Riemannian metric based on the minimum-variance prediction geometry of the underlying time-series. It is also being compared with the more traditional Itakura-Saito distance measure, as well as the aforementioned prediction metric, on two representative examples.