# Re: First moment of spectrum (Paul Boersma )

```Subject: Re: First moment of spectrum
From:    Paul Boersma  <paul.boersma(at)HUM.UVA.NL>
Date:    Tue, 13 Jun 2000 22:08:24 +0200

> I am amazed that no phonetician has so far bothered to weigh in in this
> debate, and I have not seen any psychoacoustic concerns addressed, either.

>Prey tell, what would the first moment tell about an /i/ or /u/ vowel?

[i] has the highest, [u] the lowest first moment of all vowels.
But a better single-valued approximation of these vowels is
the one-formant perceptual equivalent, which is 4000 Hz for /i/ and 300 Hz for /u/.

We can use the first moment, however, to nicely distinguish the retroflex sibilant,
the palatalized palatoalveolar sibilant, and the alveolar sibilant in Polish
(e.g. 3300 Hz, 5000 Hz, and 7400 Hz, respectively).

By the way, the following is a script to compute the first moment (magnitude-wise)
of a selected Spectrum object in the Praat program:

nbin = Get number of bins
Copy... sum
Copy... weightedSum
select Spectrum sum
# Integrate the rms power:
Formula... sqrt (self[1,col]^2 + self[2,col]^2) + self [col-1]
sum = Get real value in bin... nbin
select Spectrum weightedSum
# Integrate the rms power, weighted by frequency:
Formula... x * (sqrt (self[1,col]^2 + self[2,col]^2)) + self [col - 1]
weightedSum = Get real value in bin... nbin
firstMoment = weightedSum / sum
select Spectrum sum
plus Spectrum weightedSum
Remove
echo 'firstMoment' Hz

Of course, the values obtained may depend rather critically on the
chosen Nyquist frequency, i.e. white noise has an infinite first moment.
--

Paul Boersma
Institute of Phonetic Sciences, University of Amsterdam
Herengracht 338, 1016CG Amsterdam, The Netherlands
http://www.fon.hum.uva.nl/paul/
```

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