Filterbank reconstruction of band‐limited signals from multichannel samples associated with the LCT

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. This study addresses the problem of filterbank implementation for multichannel sampling in the LCT domain. First, the interpolation and sampling identities in the LCT domain are derived by the properties of LCT. The interpolation identity is the key result of the current study, which establishes the equivalence of two signal processing operations. One of these uses continuous-time-domain filters, whereas the other uses discrete processing. Then, applying the interpolation identity, the particularly efficient filterbank implementation for derivative sampling, periodic non-uniform sampling and multichannel sampling are obtained in the LCT domain. Moreover, the authors present filterbank implementation using polyphase structures in LCT domain. Furthermore, the simulations are carried out to verify the effectiveness of the results and the potential applications of the multichannel sampling are also presented. Finally, combining the sampling and interpolation identity, they explore the relationship between the multichannel sampling and the filterbank in the LCT domain.