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Filtering of quaternion signals

  • Theory and Methods of Signal Processing
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Abstract

Filtering of quaternion signals that specify group point objects and images in the form of polyhedrons in a 3D space is considered. It is shown that the main difference between a quaternion filter and filters for real and complex-valued signals is that, in a quaternion filter, each mth harmonic of the input signal is split into two harmonics: the reference harmonic with frequency m and the image harmonic with the frequency s-m. This behavior of the filter results from the noncommutativity of the multiplication operation for quaternions, a circumstance that necessitates the calculation of two scalar products with nonzero values at frequencies m and s-m, respectively, rather than one scalar product.

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Authors
  1. Ya. A. Furman
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  2. R. G. Khafizov
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  3. A. A. Rozhentsov
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Additional information

Original Russian Text © Ya.A. Furman, R.G. Khafizov, A.A. Rozhentsov, 2007, published in Radiotekhnika i Elektronika, 2007, Vol. 52, No. 1, pp. 42–50.

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Furman, Y.A., Khafizov, R.G. & Rozhentsov, A.A. Filtering of quaternion signals. J. Commun. Technol. Electron. 52, 36–44 (2007). https://doi.org/10.1134/S1064226907010068

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  • DOI: https://doi.org/10.1134/S1064226907010068

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