Lehmer Transform and its Theoretical Properties
This provides an alternative method for analyzing non-stationary signals like brain wave EEG, but it appears incremental as it builds on existing mean functions without demonstrated applications.
The authors introduced the Lehmer Transform, a new class of transforms based on the Lehmer mean function that decomposes a function of a sample into statistical moments, and presented its theoretical properties.
We propose a new class of transforms that we call {\it Lehmer Transform} which is motivated by the {\it Lehmer mean function}. The proposed {\it Lehmer transform} decomposes a function of a sample into their constituting statistical moments. Theoretical properties of the proposed transform are presented. This transform could be very useful to provide an alternative method in analyzing non-stationary signals such as brain wave EEG.