On the Theoretical properties of Lp mean comparators

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 L
p
comparators for which simple analog implementations exist. From a statistical point of view, the L
p
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. L
p
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.