Design of computationally efficient 2D FIR filters using sampling-kernel-based interpolation and frequency transformation

A closed-form design of a two-dimensional (2D) finite impulse response (FIR) filter with circular, rectangular, fan or quadrant-fan shapes in the passband region is presented. The computationally efficient 2D FIR filter can be implemented using frequency transformation and sampling-kernel-based interpolation instead of an optimisation algorithm. When compared with the existing method, the proposed method reduces 90% of multiplications for filtering. Several design examples are demonstrated to verify the performance of the proposed design.