Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral density function. However, unlike time series analysis, for point processes such approaches are currently underutilized. In part, this is because the interpretation of the spectral representation of point patterns is challenging. In this paper, we demonstrate how to band-pass filter point patterns, thus enabling us to explore the spectral representation of point patterns in space by isolating the signal corresponding to certain sets of wavenumbers.

翻译：空间点模式是生态学、医学、天文学、犯罪学、流行病学及众多其他应用领域中常见的数据记录形式。理解其二阶依赖结构的一种途径是通过其谱密度函数。然而，与时间序列分析不同，点过程的相关方法目前尚未得到充分利用。部分原因在于点模式谱表示的解读颇具挑战性。本文展示了如何对点模式进行带通滤波，从而通过隔离对应特定波数集的信号，实现对空间点模式谱表示的探索。