Uncertainty Principle of Ambiguity Function in Linear Canonical Transform Domain

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.