TY - GEN
T1 - Uncertainty Principle of Ambiguity Function in Linear Canonical Transform Domain
AU - Xin, Hongcai
AU - Li, Bingzhao
AU - Xie, Huiqin
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024
Y1 - 2024
N2 - The ambiguity function (AF) and its related uncertainty function are essential time-frequency analysis method for the waveform properties and echo-location in radar and optical applications. This paper devotes to investigate new uncertainty principles of AF in linear canonical transform domain (AFL) for complex-value function. Firstly, the moments of AFL are defined to measure mean and the covariance of signal in time and frequency domain. Then new uncertainty principles of AFL are proposed related to moments, which capture lower bounds for product of time delay and Doppler spreads. The lower bound can be only achieved by Gaussian-type function. Furthermore, an example with Gaussian-type function is performed to verify the correctness of proposed uncertainty principles. Finally, potential applications of derived theorems are explored in the field of radar.
AB - The ambiguity function (AF) and its related uncertainty function are essential time-frequency analysis method for the waveform properties and echo-location in radar and optical applications. This paper devotes to investigate new uncertainty principles of AF in linear canonical transform domain (AFL) for complex-value function. Firstly, the moments of AFL are defined to measure mean and the covariance of signal in time and frequency domain. Then new uncertainty principles of AFL are proposed related to moments, which capture lower bounds for product of time delay and Doppler spreads. The lower bound can be only achieved by Gaussian-type function. Furthermore, an example with Gaussian-type function is performed to verify the correctness of proposed uncertainty principles. Finally, potential applications of derived theorems are explored in the field of radar.
KW - Ambiguity function
KW - Complex-value function
KW - Linear canonical transform
KW - Moments
KW - Uncertainty principle
UR - http://www.scopus.com/inward/record.url?scp=85214435168&partnerID=8YFLogxK
U2 - 10.1109/EIT63098.2024.10762281
DO - 10.1109/EIT63098.2024.10762281
M3 - Conference contribution
AN - SCOPUS:85214435168
T3 - 2024 3rd International Conference on Electronics and Information Technology, EIT 2024
SP - 734
EP - 738
BT - 2024 3rd International Conference on Electronics and Information Technology, EIT 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 3rd International Conference on Electronics and Information Technology, EIT 2024
Y2 - 20 September 2024 through 22 September 2024
ER -