Generalized sampling theorem for bandpass signals associated with fractional Fourier transform

Abstract

The fractional Fourier transform (FRFT) which is a generalization of the Fourier transform (FT) has been shown to be a powerful analyzing tool in signal processing. Many properties of the FT including the generalized sampling theorem have been extended to the FRFT. However, the existing extensions of the classical generalized sampling theorem for the FRFT are derived from the lowpass signal viewpoint, and the implementation of those extensions is inefficient for the effect of spectral leakage. In this paper, we propose a new generalized sampling theorem associated with the FRFT from the fractional bandpass signal viewpoint. The proposed theorem which is constructed by the ordinary convolution in the time domain can overcome the effect of spectral leakage and is easy to implement in practical applications.