Non Separable 2D Sampling (Generalization):

The effective sampling grid is still rectangular when is an integer value. However the neighborhood relationship of samples no longer follow an orthogonal-axis scheme for any . Cases which can be deduced from sampling by non-integer shear factors are:

• quincunx sampling scheme,

Figure(3.2.22)

In these cases the basis vectors are tuned such that each sample has same distances towards its six or four nearest neighbors, respectively. The only free parameter is the vertical sampling distance S, but even this is predetermined by the properties of the camera in case of analog video signals. The basis vectors as shown above influence the position shifts between samples in adjacent lines.

For hexagonal and quincunx sampling this is described by matrices,

For the different sampling matrices, the layouts of the basebands and the periodic copies thereof are shown below