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 low-pass signals with FRFT. Our work is a generalization of the classical results and will enrich the theoretical system of the fractional Fourier transform.