Half-Plane and Wedge IIR Filters Based on Hyperbolic Tangent Approximation

This work presents an efficient analytic approach for the design of a particular class of 2D filters, namely half-plane and wedge filters, with a specified orientation in the frequency plane, which can be useful in building directional filter banks. The proposed method starts from the rational approximation of a very steep tanh function, to which a specific frequency mapping is applied, which leads to the desired half-plane filter with given orientation. A wedge filter with imposed orientation and aperture results as a product of the frequency responses of two half-plane filters with different angles. This entirely analytic technique uses the Chebyshev-Padé approximation and leads to efficient, precise filters, which only have marginal distortions, further removed through a wide-band correction mask filter. The designed filters result in factored frequency responses, a major advantage in implementation. Furthermore, the designed wedge filters are parametric, with adjustable orientation.