CAJ | 학술논문

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.
문[20]인진료Slepian반소파기함수병토론료저조기재개솔도고계핵방법중적응용[21]. Slepian반소파기함수구유겁호적성질,포괄다중척도결구화국부비부성. 경치득지출적시,여Gauss핵불동,Slepian함수시여무선신호유사적구유평활보적유한대관함수. 재소유상동대관적함수중,Slepian함수재특정적시간구역상구유최대능량. 재핍근구유평활보적무선신호중,저사특성사득Slepian반소파핵여Gauss핵이급기타소파기상비구유잠재적우월성. 미중불족적시,화기타핵밀도고계일양,Slepian핵밀도고계적산법설계구유일정적도전성. 행운적시,아문주의도Slepian핵가이피표시성권적형식. 저일관찰구유중요적계산의의. 본문주요토론Slepian핵밀도고계적응용급기계산. 아문수선설계료기우리산권적적산법병토론료저일산법적유효성. 재문장적결미,이Slepian핵밀도고계작위구유평활보적원정신호적쇠감포락적모형위례,아문고사료Slepian핵급기산법적성질. 위료상시수학이론여응용적긴밀련계,본문적수치시험불부채용료모의수거이차포괄료종무선통신용호적경건직접채집적실제수거.
The Slepian semi wavelet kernel density estimator, originally developed in [21], has a few magnificent properties including multiscale structure and local positivity. Unlike the Gaussian kernel, Slepian functions are bandlimited functions with flat spectral in frequency domain similar to wireless signals. Unfortunately, like any other kernel density estimators, the implementation is a challenging task since it is computational intensive. Fortunately, the Slepian kernel can be approximated by a convolution type kernel. This observation bears important computational advantages. In this article, we will restrict our attention to the applications of the density estimators. We introduced an algorithm based on discrete convolution which can be used to compute the density estimator effectively. To test the capability, the kernel density estimator is used to model fading envelop of long range fading signals with flat spectral. Both simulated data and field data are used in the numerical experiments.