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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Re: First moment of spectrum*From*: Paul Boersma <paul.boersma@xxxxxxxxxx>*Date*: Tue, 13 Jun 2000 22:08:24 +0200*Comments*: To: Pierre Divenyi <pdivenyi@MARVA4.NCSC.MED.VA.GOV>*In-reply-to*: <200006131908.MAA00207@marva4.ebire.org>*References*: <200006131908.MAA00207@marva4.ebire.org>*Reply-to*: Paul Boersma <paul.boersma@xxxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

> 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/

**References**:**First moment of spectrum***From:*Pierre Divenyi

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