Energy using Hanning window
I suspect you are talking about the Hann window, after Julius von Hann, and Blackman &amp; Tukey. Of course, a non-constant window may induce energy variations, either used as a weighted average, or a convolutional filter. This can be compensated in several ways:


by normalizing the window amplitudes
by separating tipme-portions, or signal components, like removing the mean or low-frequencies before doing the processing
by modelling the signal and applying model-based corrections. 


More would be needed on your signal to provide more precise answers. R. Lyons on a diagram on page xviii of his book Understanding Digital Signal Processing highlights the importance of windows.