Calculation of the impulse response of two-dimensional digital filter

A method for the calculation of the impulse response of quarter-plane and half-plane filters will be presented. The basic result is that the functions H
l
(Z) defined by
H(z, w) = \sum\min{l=-\infin}\max{+\infin} H_{l}(z)w^{-1}
obey a simple difference equation. The necessary initial conditions can be obtained by restrictions on the support of the impulse response. The proposed method is of theoretical and practical interest. It provides a way for the calculation of the impulse response of half-plane filters having a total half plane as support.