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It is said in discrete/digital signal processing that $r$th spectral moment of signal $x[n]$ is defined as: $$\sum_{n=-\infty}^{\infty}n^r x[n]$$ But how does this relate to usual continuous $r$th spectral moment of $x(t)$ which seems to be $$\int\limits_{f=-\infty}^{\infty}f^r|X(f)|\,\mathrm df$$ where $f$ is frequency, with $X(f)$ representing fourier transform of $x(t)$ to frequency domain? (I could have gotten coefficients and exponents wrong for the continuous one, so please feel free to correct me.)

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