Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uncertainty Principles for Quaternion Windowed Offset Linear Canonical
  Transform of Two Dimensional Signals   The offset linear canonical transform encompassing the numerous integral
transforms, is a promising tool for analyzing non-stationary signals with more
degrees of freedom. In this paper, we generalize the windowed offset linear
canonical transform for quaternion-valued signals, by introducing a novel
time-frequency transform namely the quaternion windowed offset linear canonical
transform of 2D quaternion-valued signals. We initiate our investigation by
studying some fundamental properties of the proposed transform including inner
product relation, energy conservation, and reproducing formula by employing the
machinery of quaternion offset linear canonical transforms. Some uncertainty
principles such as Heisenberg-Weyl, logarithmic and local uncertainty principle
are also derived for quaternion windowed offset linear canonical transform.
Finally, we gave an example of quaternion windowed offset linear canonical
transform.

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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph