Synthesis of N-dimensional recursive digital filters by Taylor series expansion

Using vector notation, a direct and simple technique for expressing the impulse response of a multidimensional digital filter in terms of the coefficients of its transfer function is presented. Based upon these results, rules for the propagation of coefficients in the impulse response are derived, and a synthesis procedure for obtaining a recursive transfer function to approximate a given infinite impulse response is presented. This approach is then extended. to the concept of multidimensional synthesis by partial fraction expansion.