Design method for 2-D circularly symmetric recursive filters

We propose a simple design method for a 2-D circularly symmetric IIR filter. Our filter consists of several rotated filters in cascade. Rotating filters in the Z-plane is not generally possible because irrational functions result. A separable filter is available. On the other hand, ±45° rotated filters are not available, but we can easily design rotational filters whose magnitude response are close to ±45° rotated filters from a 1-D filter. Consequently, the design method we propose in this item is simple because it uses only 1-D design methods.