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PreprintarXiv licencearXiv

Applying the convolution theorem to the two-dimensional magnetic inverse problem

  • Michael T. M. Woodley
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Abstract

A collection and clarification is given of the key mathematical details of the method of applying the convolution theorem as part of the solution to the two-dimensional magnetic inverse problem: reconstructing current density from magnetic field data. Particular emphasis is given to obtaining a closed-form solution for the Fourier transform of the convolution kernel that features in the Biot-Savart law. Having done this, the Fourier-transformed current density is obtained, via the convolution theorem, as a function of Fourier-transformed magnetic field data and other variables.

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Cite

BibTeXRIS
BibTeX
@misc{woodley2026applying,
  title = {{Applying the convolution theorem to the two-dimensional magnetic inverse problem}},
  author = {Michael T. M. Woodley},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01862},
  eprint = {2609.01862},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01862},
}
RIS
TY  - UNPB
TI  - Applying the convolution theorem to the two-dimensional magnetic inverse problem
AU  - Michael T. M. Woodley
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01862
UR  - https://arxiv.org/abs/2609.01862
AB  - A collection and clarification is given of the key mathematical details of the method of applying the convolution theorem as part of the solution to the two-dimensional magnetic inverse problem: reconstructing current density from magnetic field data. Particular emphasis is given to obtaining a closed-form solution for the Fourier transform of the convolution kernel that features in the Biot-Savart law. Having done this, the Fourier-transformed current density is obtained, via the convolution theorem, as a function of Fourier-transformed magnetic field data and other variables.
ER  -