of positive real numbers, named after Derrick Henry Lehmer,[1] is defined as: The weighted Lehmer mean with respect to a tuple
is non-negative thus this function is monotonic and the inequality holds.
The derivative of the weighted Lehmer mean is: Like a power mean, a Lehmer mean serves a non-linear moving average which is shifted towards small signal values for small
Given an efficient implementation of a moving arithmetic mean called smooth you can implement a moving Lehmer mean according to the following Haskell code.
Gonzalez and Woods call this a "contraharmonic mean filter" described for varying values of p (however, as above, the contraharmonic mean can refer to the specific case
Their convention is to substitute p with the order of the filter Q: Q=0 is the arithmetic mean.