Relationship between sampling and multirate filterbanks in the linear canonical transform domain

Multirate filterbanks have found applications in speech processing, image processing, communications, and in the development of new sampling theorems. This paper explores the relationship between sampling theorems and multirate filterbanks in the linear canonical transform (LCT) domain. The sampling identity and the interpolation identity for bandlimited signals in the LCT domain are discussed and then employed to obtain a discrete-time implementation for bandlimited signals in the LCT domain from their multichannel samples. Furthermore, we relate the multichannel sampling for bandlimited signals in the LCT domain as well as the corresponding continuous-time LCT filterbank to the discrete-time LCT filterbank, which can lead to new sampling strategies for bandlimited signals in the LCT domain.