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A follow on question form this one (What is meant by "spectral moment"?)

In answers to the above referenced question spectral moment is defined as:

$$ m_k=\int_{-\infty}^{\infty} f^k|X(f)|^2\ df $$

The limits on the integral include negative frequency. So is the negative frequency really important?

If I filter out all negative frequencies before calculating the moments will they be wrong?

If $|X_f|^2$ is symmetrical about zero then does this not mean that $m_k=0$ for all odd values of $k$?

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  • $\begingroup$ Note that your equation is wrong. You need to take the magnitude squared of the spectrum. $\endgroup$
    – MBaz
    Commented Jun 11, 2015 at 14:46
  • $\begingroup$ Ok. Edited. Thanks. How about the point of negative frequency? $\endgroup$
    – Ron
    Commented Jun 11, 2015 at 14:49

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