Periodogram of a point pattern — periodogram • SpecPP

Given a multivariate point pattern \(\underline{X} = (X_1, \ldots, X_m)\), compute the periodogram for \(X^{(i,j)}\). The indices i and j denotes the \(i\)-th and \(j\)-th individual point process (\(i,j\in\{1,2,\ldots, m\}\)). If the point pattern ppp is univariate (\(m=1\)), then set i = 1 and j = 1 to compute the periodogram.

Usage

periodogram(
  i,
  j,
  ppp,
  inten.formula = "~1",
  data.covariate = NULL,
  a = 0.025,
  return.DFT = FALSE,
  A1 = NULL,
  A2 = A1,
  ext.factor = NULL,
  endpt = 1.5,
  generate_freq. = generate_freq,
  taper. = taper,
  H.h.lambda.1. = H.h.lambda.1
)

Arguments

i: Mark index. An element in levels(spatstat.geom::marks(ppp)).
j: Mark index. An element in levels(spatstat.geom::marks(ppp)).
ppp: A point pattern of class "ppp".
inten.formula: A formula syntax in character format specifying the log-liner model for the intensity function, which is passed to ppm(). The default is constant intensity inten.formula = "~1".
data.covariate: Optional. The values of spatial covariates passed to the data argument in ppm().
a: Taper coefficient, a value within \((0,1/2)\). If a = 0, then taper is not applied. Default is a = 0.025.
return.DFT: If TRUE, also return the centered discrete Fourier transform (DFT).
A1, A2: Optional. Side lengths of the observation window.
ext.factor: Optional. If NULL (default), the frequency grid for the periodogram is not extended. Please keep this NULL unless you know what you are doing.
endpt: A positive value indicating the scale factor of the endpoint frequency.
generate_freq., taper., H.h.lambda.1.: Functions in their respective .R files.

Value

A matrix if return.DFT = FALSE; a list consisting of the periodogram and the centered DFT if return.DFT = TRUE.