On the recursive and nonrecursive realization of multidimensional discrete systems

In multidimensional (m-D) system theory, the terms "recursive" or "nonrecursive" are commonly used to denote infinite impulse response (IIR) or finite impulse response (FIR) systems, respectively. In this paper it is shown that the m-D FIR systems can be realized recursively, in addition to known nonrecursive techniques which are based on the direct convolution, while m-D IIR systems can be also realized nonrecursively. The two-dimensional (2-D) IIR quarter-plane (QP) and nonsymmetric half-plane (NSHP) filters are considered separately.