Multi-dimensional linear canonical transform with applications to sampling and multiplicative filtering

This paper presents a novel and elegant convolution structure for the multi-dimensional linear canonical transform involving a puremulti-dimensional kernel obtained via a general 2nx2n real, symplectic matrix M with n(2n+1) independent parameters. The primary intention is to develop the convolution theorem associated with the novel linear canonical convolution. The convolution structure is subsequently invoked to establish the sampling theorem for the band-limited signals in the multi-dimensional linear canonical domain. The validity and efficiency of the sampling procedure are demonstrated via a lucid example. Besides, the Heisenberg's and Beckner's uncertainty principles associated with the multi-dimensional linear canonical transform are also studied in detail. Finally, we study and design the multiplicative filter in the multi-dimensional linear canonical domain by utilizing the proposed multi-dimensional convolution structure.