Rajala, TA;
Olhede, SC;
Grainger, JP;
Murrell, DJ;
(2023)
What is the Fourier Transform of a Spatial Point Process?
IEEE Transactions on Information Theory
, 69
(8)
pp. 5219-5252.
10.1109/TIT.2023.3269514.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | What is the Fourier Transform of a Spatial Point Process? |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TIT.2023.3269514 |
| Publisher version: | https://doi.org/10.1109/TIT.2023.3269514 |
| Language: | English |
| Additional information: | © The Authors 2023. This work is licensed under a Creative Commons Attribution 4.0 License. For more information (https://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Spectral density function, Spatial point processes, Debiased periodogram, Tapering |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Div of Biosciences > Genetics, Evolution and Environment |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10171752 |
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