Computer-aided approximation of circularly symmetric two-dimensional filters obtained by starting from separable 1-D transfer functions

It is well known that perfectly circularly-symmetric 2-D digital filters cannot be implemented in practice. This paper makes an attempt to develop computer-aided approximation of circularly-symmetric 2-D digital filters. The starting point is the configuration with separable 1-D transfer functions in the forward path along with a multiplier k in the feedback path. Computer programs are developed so that when the transfer functions are prescribed, one can obtain the range of possible values of k for which the error does not exceed a prescribed value of cc percent. Different types of low-pass filters and other types of filters like high-pass, band-pass and band-elimination filters are considered as examples.