TY - JOUR
T1 - Quaternion Windowed Linear Canonical Transform of Two-Dimensional Signals
AU - Gao, Wen Biao
AU - Li, Bing Zhao
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - We investigate the 2D quaternion windowed linear canonical transform (QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift, modulation, orthogonality relation, are derived based on the spectral representation of the quaternionic linear canonical transform (QLCT). Secondly, by the Heisenberg uncertainty principle for the QLCT and the orthogonality relation property for the QWLCT, the Heisenberg uncertainty principle for the QWLCT is es- tablished. Finally, we give an example of the QWLCT.
AB - We investigate the 2D quaternion windowed linear canonical transform (QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift, modulation, orthogonality relation, are derived based on the spectral representation of the quaternionic linear canonical transform (QLCT). Secondly, by the Heisenberg uncertainty principle for the QLCT and the orthogonality relation property for the QWLCT, the Heisenberg uncertainty principle for the QWLCT is es- tablished. Finally, we give an example of the QWLCT.
KW - Quaternion linear canonical transform
KW - Quaternion windowed linear canonical transform
KW - Uncertainty principle
UR - http://www.scopus.com/inward/record.url?scp=85078663239&partnerID=8YFLogxK
U2 - 10.1007/s00006-020-1042-4
DO - 10.1007/s00006-020-1042-4
M3 - Article
AN - SCOPUS:85078663239
SN - 0188-7009
VL - 30
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 1
M1 - 16
ER -