Simple methods for the design of 2-D recursive digital filters with non-circular cutoff boundary

Several methods are presented for the design of 1-D filters with noncircular symmetric cutoff boundaries. The proposed techniques use 2-D separable product filters as the basic building blocks. Depending on the choice of the different shape cutoff boundaries, these 2-D filters are cascaded with another 2-D filter. The second 2-D filter is obtained by transformation of a 1-D filter prototype using the complex transformation. The methods presented are very simple and require no optimization. However, optimization techniques are also utilized as an improvement to the proposed schemes where higher accuracies are needed. Examples are given to illustrate the techniques