TY - JOUR
T1 - Uncertainty Principles for Wigner–Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform
AU - Urynbassarova, Didar
AU - El Haoui, Youssef
AU - Zhang, Feng
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/1
Y1 - 2023/1
N2 - Wigner–Ville distribution (WVD) associated with the quaternion offset linear canonical transform (QOLCT) (WVD–QOLCT) is the known furthest generalization of the WVD in quaternion algebra. WVD–QOLCT is a hybrid transform that combines the flexibility and results of both WVD and QOLCT. Recently, some properties and classical Heisenberg's uncertainty principle (UP) have been derived for the two-dimensional (2D) two-sided WVD–QOLCT. This paper complements it by presenting conjugation symmetry and nonlinearity properties. Then, to characterize the simultaneous localization of a signal and its WVD–QOLCT, we establish different UPs for the 2D WVD–QOLCT, such as logarithmic UP, Hardy's UP, and Beurling's UP. In the end, by using the nonlinearity property, the applications of the 2D WVD–QOLCT in the linear frequency modulated signal detection are proposed.
AB - Wigner–Ville distribution (WVD) associated with the quaternion offset linear canonical transform (QOLCT) (WVD–QOLCT) is the known furthest generalization of the WVD in quaternion algebra. WVD–QOLCT is a hybrid transform that combines the flexibility and results of both WVD and QOLCT. Recently, some properties and classical Heisenberg's uncertainty principle (UP) have been derived for the two-dimensional (2D) two-sided WVD–QOLCT. This paper complements it by presenting conjugation symmetry and nonlinearity properties. Then, to characterize the simultaneous localization of a signal and its WVD–QOLCT, we establish different UPs for the 2D WVD–QOLCT, such as logarithmic UP, Hardy's UP, and Beurling's UP. In the end, by using the nonlinearity property, the applications of the 2D WVD–QOLCT in the linear frequency modulated signal detection are proposed.
KW - Linear frequency modulated (LFM) signal
KW - Quaternion offset linear canonical transform (QOLCT)
KW - Signal detection
KW - Uncertainty principle (UP)
KW - Wigner–Ville distribution (WVD)
UR - http://www.scopus.com/inward/record.url?scp=85137006240&partnerID=8YFLogxK
U2 - 10.1007/s00034-022-02127-y
DO - 10.1007/s00034-022-02127-y
M3 - Article
AN - SCOPUS:85137006240
SN - 0278-081X
VL - 42
SP - 385
EP - 404
JO - Circuits, Systems, and Signal Processing
JF - Circuits, Systems, and Signal Processing
IS - 1
ER -