Design of Two-Dimensional FIR Fan Filters with Arbitrarily Rotated Frequency Response

Abstract

This paper presents a design method of the zero phase two-dimensional (2-D) finite impulse response (FIR) fan filters having rotated frequency response of a given prototype fan filter. The first step of our approach is to design a prototype filter with the impulse response whose domain is restricted within a circular region. This restriction prevents rotated impulse array to moving out from the rectangular region. Then, the rotation of prototype impulse response, which is given no more than on the rectgngular lattice grid, may cause the same rotation in the frequency domain. The second step is the interpolation of the impulse response on the new grids by the reconstruction algorithm of 2-D bandlimited discrete signals. Previous other methods for the rotation and the interpolation are compared with the proposed method. The obtained results for fan-type filter approximation by the proposed method show its validity.