线性正则变换域的带限信号采样理论研究

Sampling Theories of Bandlimited Signals in Linear Canonical Transform Domain

线性正则变换是傅里叶变换、分数阶傅里叶变换的更广义形式,是一种潜在而重要的信号变换工具,但是与之相应的采样理论目前还不十分完备,所以有必要在线性正则变换域重新研究采样定理.本文从线性正则变换的定义和性质出发,首先得到时域均匀采样信号的线性正则变换;然后在此基础上导出了线性正则变换域带限信号的采样定理和重构公式;最后以chirp信号为例仿真说明了采样定理的应用.文中得出的结论是对经典采样理论的推广,将进一步丰富线性正则变换的理论体系.

The linear canonical transform（LCT） is a generalization of the Fourier transform and the fractional Fourier transform（FRFT）.It is a potential but powerful tool for signal transformation.The sampling theories related to LCT have not been completed yet,so the sampling theorem needs to be restudied in the LCT domain.We first briefly introduce the LCT and its properties,then obtain the LCT of the uniform sampled signals in time domain and based on it,we deduce sampling theorem and reconstruction formula for bandlimited signals with LCT.Finally,an example of sampling a chirp signal is provided to demonstrate the application of the sampling theorem.Our work is a generalization of the classical sampling theories and will enrich the theoretical system of the linear canonical transform.