Spectrum: Get centre of gravity...

A command to query the selected Spectrum object.

If the complex spectrum is given by S(f), where f is the frequency, the centre of gravity is given by

 ∫0∞ f |S(f)|p df

divided by the "energy"

 ∫0∞ |S(f)|p df

Thus, the centre of gravity is the average of f 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.

### Setting

Power
the quantity p in the formulas above. Common values are 2, 1, or 2/3.

### Interpretation

The spectral centre of gravity is a measure for how high the frequencies in a spectrum are on average. For a sine wave with a frequency of 377 Hz, the centre of gravity is 377 Hz. You can easily check this in Praat by creating such a sine wave (Create Sound from formula...), then converting it to a Spectrum (Sound: To Spectrum...), then querying the mean frequency. For a white noise sampled at 22050 Hz, the centre of gravity is 5512.5 Hz, i.e. one half of the Nyquist frequency.

### Related measures

The centre of gravity is used in the computation of spectral moments: