Multichannel sampling and reconstruction of bandlimited signals in the linear canonical transform domain

Abstract

Multichannel sampling for bandlimited signals is fundamental in the theory of multichannel parallel analogue-to-digital (A/D) environment and multiplexing wireless communication environment. The analysis and application of multichannel sampling in the traditional Fourier domain have been extensively studied, but so far none of the research papers covering the reconstruction of multichannel sampling in the linear canonical transform (LCT) domain have been published. This study is to explore the multichannel sampling and reconstruction of bandlimited signals in the LCT domain. First, the multichannel sampling theorem for bandlimited signals with LCT is proposed, which is the generalisation of classical generalised Papoulis sampling expansion. Considering the signal reconstruction purpose, the authors present two schemes for the multichannel sampling with LCT. The first scheme is based on the conventional Fourier series and inverse LCT, whereas the other uses the generalised convolution systems. Second, by designing different LCT filters, the authors obtain the reconstruction method for the uniform sampling theorem, sampling from the signal and its derivative by using the derived multichannel sampling theorem and properties of the LCT. Last, the simulations are carried out to verify the correctness of the results. Moreover, the potential applications of the multichannel sampling are also presented.