Vector Sampling Expansions and Linear Canonical Transform

In a vector sampling expansion (VSE), N signals bandlimited to W rad/s in the conventional Fourier domain (CFD) pass through multi-input multi-output (MIMO) linear time-invariant (LTI) systems and produce M ≥ N output bandlimited signals in the CFD. In the uniformly sampled VSE, the outputs of all the M systems are uniformly sampled at the same rate while preserving the total number of samples per second equal to NW/π. In the literature, a necessary condition for perfect signal reconstruction in such a uniformly sampled VSE is discussed which requires M/N to be an integer. It is the purpose of this paper to demonstrate that use of linear canonical transform (LCT) in uniformly sampled VSE allows perfect signal reconstruction even when M/N is not an integer.