Two-dimensional hexagonal digital recursive filters

It is known that band-limited two-dimensional (2D) signals can be sampled and processed using different periodic sampling strategies, the most common and perhaps well known approach being rectangular sampling. Recently, it has been pointed out that sampling techniques such as hexagonal sampling can offer substantial savings in terms of sampling density and computation time as compared to rectangular sampling. In this paper, we examine in detail, the design of recursive systems for processing of such hexagonally sampled 2D signals. It is shown that a method previously developed by the author for the design of rectangular recursive filters can be used for hexagonal recursive filter design, as well. The method guarantees the stability of the filters designed. Examples of hexagonal recursive filters designed using this method are given.