High frequency content measure

In signal processing, the high frequency content measure is a simple measure, taken across a signal spectrum (usually a STFT spectrum), that can be used to characterize the amount of high-frequency content in the signal. The magnitudes of the spectral bins are added together, but multiplying each magnitude by the bin "position" (proportional to the frequency). Thus if X(k) is a discrete spectrum with N unique points, its high frequency content measure is:

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