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PreprintCC BY 4.0PsyArXiv

The relationship between numerosity and the Fourier power spectrum of dot arrays

  • Joonkoo Park
  • Shimin Hu
  • Ruoyu Yuan
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Abstract

This technical note presents mathematical derivations that establish the relationship between numerosity and the Fourier power spectrum of dot arrays, a standard stimulus in biological and psychological research in numerosity perception (e.g., DeWind et al. (2015); Park and Huber (2022). We derive a closed-form solution for the radially averaged power spectrum of images depicting arrays of identical dots as a function of dot number, radius, spacing, and spatial frequency. We also demonstrate that an unconventional distillation of the Fourier coefficients, as done in Paul et al. (2022), reveals an artifactual relationship between that metric and numerosity.

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Cite

BibTeXRIS
BibTeX
@misc{park2026relationship,
  title = {{The relationship between numerosity and the Fourier power spectrum of dot arrays}},
  author = {Joonkoo Park and Shimin Hu and Ruoyu Yuan},
  howpublished = {PsyArXiv},
  year = {2026},
  month = sep,
  doi = {10.31234/osf.io/zs82e_v1},
  url = {https://osf.io/preprints/psyarxiv/zs82e_v1/},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The relationship between numerosity and the Fourier power spectrum of dot arrays
AU  - Joonkoo Park
AU  - Shimin Hu
AU  - Ruoyu Yuan
PY  - 2026
DA  - 2026/09/21
PB  - PsyArXiv
DO  - 10.31234/osf.io/zs82e_v1
UR  - https://osf.io/preprints/psyarxiv/zs82e_v1/
AB  - This technical note presents mathematical derivations that establish the relationship between numerosity and the Fourier power spectrum of dot arrays, a standard stimulus in biological and psychological research in numerosity perception (e.g., DeWind et al. (2015); Park and Huber (2022). We derive a closed-form solution for the radially averaged power spectrum of images depicting arrays of identical dots as a function of dot number, radius, spacing, and spatial frequency. We also demonstrate that an unconventional distillation of the Fourier coefficients, as done in Paul et al. (2022), reveals an artifactual relationship between that metric and numerosity.
ER  -