Convolution and correlation theorems for the two-dimensional linear canonical transform and its applications

Convolution and correlation operations are very important in signal processing community, as well as in sampling, filter design and applications. In this study, the authors derive the convolution and correlation theorems for the two-dimensional linear canonical transform (2D LCT). Moreover, they utilise the convolution theorem to investigate the sampling theorem for the band limited signal in the 2D LCT domain. They also discuss multiplicative filter for the band limited signal in the 2D LCT domain which has much lower computational load than the method in the 2D LCT domain.