
A command to query the selected Spectrum object.
If the complex spectrum is given by S(f), the nth central spectral moment is given by
∫_{0}^{∞} (f – f_{c})^{n} S(f)^{p} df 
divided by the "energy"
∫_{0}^{∞} S(f)^{p} df 
In this formula, f_{c} is the spectral centre of gravity (see Spectrum: Get centre of gravity...). Thus, the nth central moment is the average of (f – f_{c})^{n} over the entire frequency domain, weighted by S(f)^{p}. For p = 2, the weighting is done by the power spectrum, and for p = 1, the weighting is done by the absolute spectrum. A value of p = 2/3 has been seen as well.
For n = 1, the central moment should be zero, since the centre of gravity f_{c} is computed with the same p. For n = 2, you get the variance of the frequencies in the spectrum; the standard deviation of the frequency is the square root of this. For n = 3, you get the nonnormalized spectral skewness; to normalize it, you can divide by the 1.5 power of the second moment. For n = 4, you get the nonnormalized spectral kurtosis; to normalize it, you can divide by the square of the second moment and subtract 3. Praat can directly give you the quantities mentioned here:
© ppgb, March 23, 2002