Analytical design of frequency scaled asteroidal 2-D FIR filters

Novel approach to the analytical design of frequency scaled asteroidally shaped two-dimensional FIR filters is presented. The design consists of two steps. In the first step, the basic fourfold symmetrical asteroidal 2-D FIR filter 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 basic filter is scaled along both frequency coordinates. Closed form formula for the calculation of the impulse response of the scaled filter is presented. One example demonstrates both steps of the design procedure.