Reconstruction of band-limited signals from multichannel and periodic nonuniform samples in the linear canonical transform domain

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. This paper addresses the problem of signal reconstruction from multichannel and periodic nonuniform samples in the LCT domain. Firstly, the multichannel sampling theorem (MST) for band-limited signals with the LCT is proposed based on multichannel system equations, which is the generalization of the well-known sampling theorem for the LCT. We consider the problem of reconstructing the signal from its samples which are acquired using a multichannel sampling scheme. For this purpose, we propose two alternatives. The first scheme is based on the conventional Fourier series and inverse LCT operation. The second is based on the conventional Fourier series and inverse Fourier transform (FT) operation. Moreover, the classical Papoulis MST in FT domain is shown to be special case of the achieved results. Since the periodic nonuniformly sampled signal in the LCT has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived MST and the specific space-shifting property of the LCT. Last, the potential applications of the MST are presented to show the advantage of the theory.