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We investigate the 2D quaternion windowed linear canonical transform(QWLCT)in this paper. Firstly, we propose the new definition of the QWLCT, and thenseveral important properties of newly defined QWLCT, such as bounded, shift,modulation, orthogonality relation, are derived based on the spectralrepresentation of the quaternionic linear canonical transform(QLCT). Finally,by the Heisenberg uncertainty principle for the QLCT and the orthogonalityrelation property for the QWLCT, the Heisenberg uncertainty principle for theQWLCT is established.

Quaternion Windowed Linear Canonical Transform of Two-Dimensional Quaternionic Signals