  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.
