On the synthesis of a class of 2-D acausal lossless digital filters

Passive and lossless two-dimensional (2-D) discrete systems of the fully recursive half-plane type are reviewed as one-dimensional (1-D) filters over convolutional algebra. Necessary and sufficient conditions for 2-D transfer functions to be valid scattering as well as immittance description of such systems are obtained. An algorithm for the structurally passive (in fact, lossless) synthesis of filters having such recursive structure is then derived from these representation results as an extension of a recent 1-D Schur-type algorithm for the synthesis of discrete lossless two-ports. Comments on various aspects of design and implementation of such 2-D filters potentially useful in practical problems are also made