For a FFT result in frequencies $k$ and associated amplitude magnitude $A(k)$ it is possible to calculate the signal energy by: $E=\sum_{k=1}^{N} A(k)^2 $
However, what does it mean when the energy is multiplied by the current frequency $k$ such as:
$E=\sum_{k=1}^{N} k\:A(k)^2 $
I thought it is a way to calculate frequency energy, but cannot find any source doing it this way. If it is a viable calculation, is there a name for this method?