Abstract:
Narrow-band signal are widely used in radar,sonar,communication,positioning,biomedical engineering and other fields.The sampling and reconstruction formula of narrow-band signal in the Fourier Transform domain have been studied in traditional sampling theorem.The Linear Canonical Transform (LCT) is a generalization of the Fourier Transform and the Fractional Fourier Transform (FrFT).And the sampling theories related to it have not been completed yet,so the sampling theorem for narrow-band signal needs to be restudied in the LCT domain.Starting from the definition and property of LCT,we first introduce the Hilbert transform related to LCT,then obtain the representation of narrow-band signal in LCT domain and based on it,we deduce sampling theorem and reconstruction formula for narrow-band signal with LCT.Our work is a generalization of the classical results and will enrich the theoretical system of the Linear Canonical Transform.Finally,simulation results further validate the correctness of the conclusion.