Multichannel Consistent Sampling and Reconstruction Associated with Linear Canonical Transform

Multichannel sampling is fundamental in the theory of multichannel parallel analog-to-digital converters and multiplexing wireless communication. This letter investigates the multichannel consistent sampling theory associated with the linear canonical transform, which can combine the reconstruction of the signal and the correction of sensor distortions. The consistency requests that a resampling of the reconstruction by the original sampling operation yields the same measurements as before. The consistent sampling is applicable to an arbitrary finite energy signal and without the constraint such as band-limiting. Under this circumstance, two effective reconstruction methods based on the shift-invariant reconstruction space and the linear canonical basis functions space are developed. Finally, the reconstruction experiment of the radar echo signal is presented.