On the analysis of sorting networks from the viewpoint of circuit theory

A sorting network is the kernel of an order statistics-based filter and contains all information about the nonlinearity. Its implementation is simple; its analysis, however, is relatively difficult due to the hiding of the nonlinearity. In this short paper, we analyze a sorting network from the viewpoint of classical circuit theory, and reveal its relation to a nonlinear lossless n-port. We show that a sorting network is in fact the wave digital filter (WDF) realization of an n-port memoryless nonlinear classical network. Hence, it can be unified to the group of nonlinear WDF networks. Useful properties such as passivity and losslessness are hence inherent properties of such networks.