分数阶傅里叶变换域上带通信号的采样定理

傅里叶变换和采样定理是信号处理领域的两大基本问题,采样定理研究了傅里叶变换域上带限信号的采样和重构理论.分数阶傅里叶变换(FRFT)是傅里叶变换的一种推广,与之相应的采样理论目前还不十分完备,所以有必要从FRFT域上重新研究采样定理.本文首先得到了均匀冲激串采样信号的FRFT,然后在此基础上导出了FRFT域上带通信号和低通信号的采样定理和重构公式.这些结果是经典理论的推广,将丰富分数阶傅里叶变换的理论体系.

Sampling Theorems for Bandpass Signals with Fractional Fourier Transform

Fourier transform and sampling theorem are the two fundamental problems in signal processing fields.The traditional sampling theorem clarifies the sampling and reconstruction theories of the bandlimited signals with Fourier transform.The fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform.And the sampling theories related to it have not been completed yet,so the sampling theorem needs to be restudied in the FRFT domain.In this paper,we first obtain the FRFT of the uniform impulse-train sampled signals,and based on it,we deduce sampling theorem and reconstruction formula for bandpass and lowpass signals with FRFT.Our work is a generalization of the classical results and will enrich the theoretical system of the fractional Fourier transform.