Compute \(\hat{H}^{(n)}_{h\hat{\lambda}^{(i)},1}\) in the centered DFT

This function computes $$\hat{H}^{(n)}_{h\hat{\lambda}^{(i)},1}(\boldsymbol\omega) = \int_{D_n}h(\boldsymbol{x}/\boldsymbol{A})\hat{\lambda}^{(i)}(\boldsymbol{x}) \exp(-i\boldsymbol{x}^\intercal\boldsymbol\omega)d\boldsymbol{x}$$ for the \(i\)th point process, \(i\in\{1,2,\ldots,m\}\).

Usage

H.h.lambda.1(w2, w1, a, taper, A1, A2, inten.fitted)

Arguments

w1, w2

A numeric value or vector of frequency values at horizontal and vertical directions, respectively.

a

Taper coefficient, a value within \((0,1/2)\). If a = 0, then taper is not applied, i.e., \(h(\boldsymbol{x}/\boldsymbol{A}) = 1\).

taper

Data taper function \(h\).

A1, A2

Side lengths of the observation window.

inten.fitted

Fitted intensity function of individual point pattern, \(\hat{\lambda}^{(i)}(\cdot)\).

Value

A value.