Nonseparable sampling theorems for two-dimensional signals

It is well-known that continuous time bandlimited signals can be sampled without creating aliasing if the sampling period is small enough. It is also known that if x(t) is a bandpass signal, the passbands of X(Ω) must be located properly for alias-free maximal sampling. Similar situations arise in discrete time case. This paper addresses these issues for two-dimensional (2D) one- and two-parallelogram signals, which are respectively the classes of 2D signals (continuous or discrete time) whose Fourier transforms have supports consisting of one and two parallelograms. In this paper, we derive necessary and sufficient conditions such that a one- or two-parallelogram signal (continuous and discrete time) allows maximal alias-free sampling