Analytical design of arbitrary oriented asteroidal 2-D FIR filters

A novel approach to the analytical design of asteroidally shaped two-dimensional FIR filters with arbitrary orientation of the frequency response in the frequency plane is presented. The design consists of two steps. In the first step, the asteroidal 2D FIR filter in the basic position along the frequency coordinates is designed. The design is based on the analytical contour approximation using the parametric representation of the contour. Closed form formulas for the approximation of the contour with asteroidal shape were derived. In the second step, the asteroidally shaped FIR filter is rotated by the desired angle in the frequency plane. Closed form formulas for the calculation of the impulse response of the filter are presented. One example demonstrates both steps of the design procedure.