The role of passivity and losslessness in multidimensional digital signal processing-new challenges

It is suggested that specified robustness criteria and the sensitivity requirement in multidimensional signal processing can be satisfied using a design based on concepts of passivity (including incremental passivity) and losslessness. The resulting algorithms represent what can be called discrete passive dynamical systems. The underlying principles are the same for multidimensional (MD) wave digital filters, and, adopting some plausible assumptions, it appears that there does not exist any other way to generate useful 1-D or MD discrete passive dynamical systems. A wide field of new applications has been opened up recently by applying these principles to numerical integration of partial differential equations. It is shown how the principles presented can be applied to various types of electrical partial differential equations (including Maxwell's equations) and to the partial differential equations of acoustics