Multichannel Sampling and Reconstruction of Bandlimited Signals in Fractional Fourier Domain

The classical multichannel sampling theorem for common bandlimited signals has been extended differently to fractional bandlimited signals associated with the fractional Fourier transform (FRFT). However, the implementation of those existing extensions is inefficient because of the effect of spectral leakage and hardware complexity. The purpose of this letter is to introduce a practical multichannel sampling theorem for fractional bandlimited signals. The theorem which is constructed by the ordinary convolution in the time domain can reduce the effect of spectral leakage and is easy to implement. The classical multichannel sampling theorem and the well-known sampling theorem for the FRFT are shown to be special cases of it. Some potential applications of this theorem are also presented. The validity of the theoretical derivations is demonstrated via simulations.