# Generalized/Power means in DSP

Generalized/power means may be used to construct moving-average filters with different properties than regular one which is based on arithmetic mean. This observation seems to be trivial - even Wikipedia mentions that. The problem is that power means are usually defined for sets of positive numbers - while in DSP we often deal with negative numbers too. Therefore, many of well-known inequalities and properties of power means may not be applied to sets with negative numbers.

This is of interest to me since I have found that in my partical area of application power means of higher order give better results than arithmetic mean. I have been able to prove some basic properties and I more or less understand where does the improvement come from. However, I would be interested in learning. However, everything I have found seems to focus on positive numbers. So my question is:

Are there any papers on using generalized means for moving average filtering or some other signal processing? Any papers on purely mathematical properties of generalized means for sets with negative values may be relevant too. Thanks!