Analytical Design of Elliptically-Shaped 2D Recursive Filters

Abstract

This paper presents an analytic design technique for 2D IIR filters with elliptical symmetry, which have useful applications in image processing. The design is based on efficient elliptic digital filters, regarded as 1D prototypes, to which specific complex frequency transformations are applied; this allows to obtain directly a factored form of the transfer function for the 2D elliptically-shaped filter. The design procedure uses accurate approximations, but no global optimization algorithm. Finally the 2D filter matrices are obtained. The filter is adjustable, its coefficients depending explicitly on the specified orientation and bandwidth. Another advantage is versatility, since the design need not be resumed each time from the start for various specifications. The designed 2D filters have an accurate elliptical shape with low distortions even close to the frequency plane margins, being efficient, of high selectivity and low order.