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I am trying to plot short time energy of an utterance with percent overlap as an input variable.

As I referred to the short time energy equation it can be represented as square summation of $x(n)*w(n-m)$ where $w(n)$ seems to be window length. But I couldn't figure out how to write it as percent overlap.

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Percent overlap merely sets how often you measure the energy, relative to the window width. You can re-measure every sample, or once per annum, or any density in between.

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The amount of overlap and the window length are completely independent parameters, other than the fact that the window has to be longer than the amount of overlap of course. People often have the window length be twice the amount of overlap (i.e. overlap = 50%), but you don't have to do that.

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