Sorting network: its nonlinear wave digital filter network equivalent

A sorting network is the kernel of an order statistics based filter that contains all informations about the nonlinearity. Its implementation is simple; its analysis, however, is relatively difficult due to the hidden nature of the nonlinearity. In this paper, we reveal that a sorting network is equivalent to a wave digital filter (WDF) network. In fact, a sorting network for n data is equivalent to an n-port memoryless nonlinear WDF network. The useful properties such as passivity and losslessness are hence the inherent properties of such networks