Connecting spatial and frequency domains for the quaternion Fourier transform

H. De Bie, N. De Schepper, T.A. Ell, K. Rubrecht and S.J. Sangwine

Applied Mathematics and Computation, 2015, vol. 271, issue C, 581-593

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.

Keywords: Quaternion Fourier transform; Convolution products; Frequency domain; Spatial domain (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:581-593

DOI: 10.1016/j.amc.2015.09.045

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