2-D FIR filter design: What shape is the best ?

In this paper, we compare minimax designs of 2-D FIR filters whose passbands and stopbands have four shapes: rectangular, diamond, circle and cos-oval. The experiments show that, when all the other design specifications (areas of pass-band and stopband, passband error bound) coincide, the cos-oval shape is usually better for narrow passbands. For such passbands, the cos-oval shape is very similar to the circular shape, but gives better stopband attenuations. Hence, it constitutes an interesting alternative for practical designs.