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Connecting spatial and frequency domains for the quaternion Fourier transform

Author

Listed:
  • De Bie, H.
  • De Schepper, N.
  • Ell, T.A.
  • Rubrecht, K.
  • Sangwine, S.J.

Abstract

The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency domains: the convolution of two quaternion signals does not map to the pointwise product of their qFT images. The recently defined ‘Mustard’ convolution behaves nicely in the frequency domain, but complicates the corresponding spatial domain analysis.

Suggested Citation

  • De Bie, H. & De Schepper, N. & Ell, T.A. & Rubrecht, K. & Sangwine, S.J., 2015. "Connecting spatial and frequency domains for the quaternion Fourier transform," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 581-593.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:581-593
    DOI: 10.1016/j.amc.2015.09.045
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    Cited by:

    1. Morais, J. & Ferreira, M., 2023. "Hyperbolic linear canonical transforms of quaternion signals and uncertainty," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    2. Siddiqui Saima & Bingzhao Li & Samad Muhammad Adnan, 2022. "New Sampling Expansion Related to Derivatives in Quaternion Fourier Transform Domain," Mathematics, MDPI, vol. 10(8), pages 1-12, April.

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