Foundations of Two-Dimensional Signal Processing

It is well known that the important of the Two-Dimensional (2-D) digital filters in the industry fields, like as the image processing. Frequency transformation is a useful method to design another types of 2-D digital filters from a given filter generally low-pass, but sometimes we need to reduce the order of the filter in terms of cost. For this to design a new type filter and with a low order, from a given filter it must to used the combination frequency transformation and Model Order Reduction (MOR), so two approaches are defined the first one is to use the frequency transformation then to apply the MOR, the second is vice versa, MOR then the frequency transformation.