# How to distinguish female and male voices via Fourier analysis?

What makes one, without looking, be able to identify the gender of the talker as male or female?

I mean if we Fourier analysed the voice of males and females, how the 2 spectrums are different which account for that distinction in sounds?

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Is this on topic for us? I can definitely see a question about the physical reasons for these differences being on topic here, but I'm not sure about just asking what the difference are. If this is off topic here it could be migrated to Signal Processing. – David Z Jan 5 '12 at 21:03
@DavidZaslavsky It is a general physics question, which came up in a course on mathematical physics. I am not an expert, hence it is pointless to ask this in a whole separate stackexchange branch. – Revo Jan 5 '12 at 23:06
Possible duplicates: physics.stackexchange.com/q/15385/2451 and link therein. – Qmechanic Jul 12 at 1:01

This has been extensively studied in linguistics and acoustics. Humans and other primates predict speaker gender through a combination of fundamental frequency $F_0$ ("pitch") and Vocal-Tract-Length estimates ($VTL$) which are a proxy for body size.

Sometimes "formant dispersion" is used for $VTL$. It is usually defined as $$\frac{\sum_{i=1}^n(F_{i+1}-F_i)}{n-1}$$where $F_i$ is the $i$th formant frequency and $n$ is the number of formants measured. However this measure is problematic and does not capture information about midrange formants or about formant positioning. See Masculine voices signal men's threat potential in forager and industrial societies

An alternative $VTL$ measure is 'formant position', defined as:$$\frac{\sum_{i=1}^nF'_i}{n}$$where $F'_i$ is the $i$th formant standardized across the population measured.

However, the usual finding is that a combination of pitch and estimates of vocal tract length give us information about speaker gender and sexual maturity. Looking at male vs female spectra, on average you'd see male voices lower-pitched and and more closely-spaced formants.

Acoustic correlates of talker sex and individual talker identity are present in a short vowel segment produced in running speech

Vocal Tract Length Perception and the Evolution of Language

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Can spectral analyses of the voice diagnose vocal problems and deasease? I am familiar with Fourier series and Fourier transform in general, unfortunately I am not familiar with "format dispersion" – Revo Jan 5 '12 at 20:21
"Formant dispersion" is a term of art in the field of auditory acoustics/linguistics. Formants are a key concept there. Formants are the spectral peaks of the voice sound, see en.wikipedia.org/wiki/Formant. In linguistics they're used to characterize and distinguish vowel and other continuant sounds and to analyze consonants by their impact on adjacent formants. – Mark Beadles Jan 5 '12 at 20:27
Yes, they are used extensively in looking vocal dysfunction as well. a google search for "formants vocal dysfunction" is quite revealing! – Mark Beadles Jan 5 '12 at 20:29
Note that the human ear works by means of what is essentially a mechanically-performed spectral analysis via something like a continuous wavelet transform. Did a paper on this for neurolinguistics once :) – Mark Beadles Jan 5 '12 at 20:35
Great information. Thank you so much. If I want to look for what kind of research is done in this field or related fields, what key words should I use? – Revo Jan 5 '12 at 20:38

My impression would be that the lower frequencies are more apparent in the male spectrum than the female spectrum.

If you want to build a nice test, my approach would be to determine some average male and average female spectrum. Then you can see which of your average or most common spectrum correlates best the test person.

However, you should take are about the noise in the measured spectrums

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You may want to investigate whether the fact that you can usually identify when a voice is a male speaking in falsetto can be explained by some particular differences from the spectrum of a female speaker. – Niel de Beaudrap Jan 5 '12 at 13:15