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文[20]引进了Slepian半小波基函数并讨论了这组基在概率度估计核方法中的应用[21].Slepian半小波基函数具有极好的性质,包括多重尺度结构和局部非负性.更值得指出的是,与Gauss核不同,Slepian函数是与无线信号类似的具有平滑谱的有限带宽函数.在所有相同带宽的函数中,Slepian函数在特定的时间区域上具有最大能量.在逼近具有平滑谱的无线信号中,这些特性使得Slepian半小波核与Gauss核以及其他小波基相比具有潜在的优越性.美中不足的是,和其他核密度估计一样,Slepian核密度估计的算法设计具有一定的挑战性.幸运的是,我们注意到Slepian核可以被表示成卷积形式.这一观察具有重要的计算意义.本文主要讨论Slepian核密度估计的应用及其计算.我们首先设计了基于离散卷积的算法并讨论了这一算法的有效性.在文章的结尾,以Slepian核密度估计作为具有平滑谱的远程信号的衰减包络的模型为例,我们考查了Slepian核及其算法的性质.为了尝试数学理论与应用的紧密联系,本文的数值试验不仅采用了模拟数据而且包括了从无线通讯用户的硬件直接采集的实际数据.
Wen et al. [20] introduced the Slepian semi-wavelet basis function and discussed the application of this group in the kernel estimation of probability [21]. The Lepian semi-wavelet basis function has excellent properties including multi-scale structure and local nonnegative It is worth pointing out that, unlike the Gauss kernel, the Slepian function is a finite bandwidth function with a smooth spectrum similar to a wireless signal. The Slepian function has the maximum energy over a particular time region for all functions of the same bandwidth. These characteristics make Slepian semi-wavelet kernels potentially superior to Gauss kernels and other wavelet bases in wireless signals with smooth spectra.The only drawback is that, as with other kernel density estimation, Slepian kernel density estimation algorithms have a certain design Fortunately, we note that the Slepian kernel can be expressed as a convolution form.This observation is of great computational significance.This paper mainly discusses the application of Slepian kernel density estimation and its calculation.Firstly, we design a method based on discrete volume Product algorithm and discusses the validity of this algorithm.At the end of the paper, the Slepian kernel density is estimated as a long-range signal with a smooth spectrum For example, we study the properties of Slepian kernel and its algorithm.In order to test the close relationship between mathematical theory and application, the numerical experiment in this paper not only uses the simulation data but also includes the direct acquisition from the wireless communication user’s hardware The actual data.