Linear and externally-bilinear multidimensional systems

Linear q-dimensional (q-D) systems and externally-bilinear q-D systems are investigated. Externally-bilinear q-D systems arise in the study of multidimensional signal processors containing signal multipliers. For example, it is shown that the cross-correlation between two locally-stationary 2-D signals can be computed using an externally-bilinear 2-D system. A class Lq of linear q-D systems and a class Bq of externally-bilinear q-D systems are defined and then a 1-1 and onto correspondence is constructed between Bq and L2q for each fixed positive integer q. Via this correspondence, it is shown that results on stability and recursive realizations of a linear 2q-D system can be carried over to the corresponding externally-bilinear q-D system.