Theoretical Analysis of Mean Comparators

In certain signal processing applications there is a need for fast implementations of sorting networks. Digital implementations of sorting networks that rely on a Digital Signal Processor core are not as efficient as their analog counterparts. This paper deals with the comparators for which simple analog implementations exist that employ operational amplifier-based adders, logarithmic and antilogarithmic multipliers. From a statistical point of view, the comparators are based on the nonlinear means. Their probability density function and the first and second-order moments are derived for independent uniformly distributed inputs. comparators provide estimates of the minimum and maximum of their inputs. Therefore, they introduce errors. A proper approach to compensate for the estimation errors is proposed.