Analog rank filtering

Abstract

The main task in rank filtering and many other nonlinear filtering operations is sorting. In this work, a nonlinear dynamical system for this operation is proposed. The sorting problem is embedded in a higher dimensional matrix-valued problem. An equivalent analog circuit consists of basic building blocks like adders, multipliers, and integrators which set up basic nonlinear processing cells. These processing cells are locally connected in a one-dimensional array of length N for a rank filter, with N input data elements taken as the initial values of the dynamical system. The time for sorting can be estimated theoretically and indicates fast convergence. In time complexity, the algorithm is of O(N). As opposed to a digital rank filter, the analog rank filter possesses a parameter to control the speed of convergence and the accuracy.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>