bartletts_spectral_density: Bartlett's spectral density

In antiphon/Kdirectional: Analysis of anisotropy in point patterns using second order statistics

Bartlett's spectral density

Description

Periodogram estimator

Usage

bartletts_spectral_density(x, omega, ...)

Arguments

x	point pattern, list of $x and $bbox
omega	The frequencies
...	ignored

Details

We estimate the spectral density using a periodogram as suggested by Bartlett 1964,

\mathcal{F}(ω) = λ + λ^2\int_{R^d}[g(z)-1]e^{-iω^T z}dz

where we assume that the process is stationary with intensity lambda and pair correlation function $g$. Isotropy is not assumed.

This function deliberately does not scale or assume a form for the frequencies (such as 2kpi/n, k integer), as there is no consensus on the best form.

Additionally, no scaling or other transformation of the pattern is conducted.

The frequencies that the spectrum is estimated are given by omega:

1) If omega is a vector, we expand it to d-dimensional frequencies using expand.grid.

2) If omega is a column matrix of dimension m x d, each row is interpreted as a frequency.

No edge correction is applied as none is known. The

antiphon/Kdirectional documentation built on Feb. 13, 2023, 6:26 a.m.