论文标题
空间点过程的傅立叶变换是什么？
What is the Fourier Transform of a Spatial Point Process?
论文作者
论文摘要
本文确定了如何在分析观察到的空间点过程时定义离散实现的傅立叶变换。为了发展这个转变，我们回答了四个问题。首先，傅立叶变换的自然定义是什么，其光谱矩是什么，其次，我们使用坎贝尔定理计算傅立叶变换的第四阶矩。第三，我们确定如何实现锥度，这是对其他随机过程的光谱分析的重要组成部分。第四，我们回答了如何产生该过程傅立叶变换的各向同性表示的问题。这决定了观察到的空间点过程的基本光谱特性。
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier transform, and what are its spectral moments, second we calculate fourth order moments of the Fourier transform using Campbell's theorem. Third we determine how to implement tapering, an important component for spectral analysis of other stochastic processes. Fourth we answer the question of how to produce an isotropic representation of the Fourier transform of the process. This determines the basic spectral properties of an observed spatial point process.
