Recursive implementation of factorable two-dimensional digital filters

A brief tutorial background on the design of two-dimensional digital filters is presented. A technique for designing stable two-dimensional recursive filters is summarized and an algorithm useful for controlling the cutoff frequencies is discussed. The problem of implementation of two-dimensional infinite impulse-response digital filters is then considered and an algorithm is proposed for filters which are factorable into bilinear second-order sections with complex coefficients. Computational errors due to the finite wordlength of the filters are analyzed. These errors can be represented by a set of error sequences additively contaminating the output of an ideal realization. The transfer functions relating these error sequences to simple roundoff errors are derived. The problems of data management when large matrices are stored in auxiliary storage are also discussed and a solution is proposed.