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The term frequency for a periodic wave can be defined as the number of times a repeating pattern occurs in a given time period (eg: no. of crest and trough cycles per second for EM wave). But what does frequency mean in the context of a human voice? I was trying to understand Modulation (out of interest) and human voice is plotted with time of $x$-axis and amplitude on $y$-axis. And amplitude/frequency of carrier is modulated based on amplitude of the input signal. Where is frequency dimension? Can someone please help me here?

Really sorry about typo in the previous version of the question. I meant to understand the frequency dimension in a typical human voice and not really interested about exact values. More specifically, if frequency of voice is plotted against time, how does the graph look? And, in general graphical representation of voice, what is plotted against time, frequency of amplitude?

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3 Answers

Unless someone is signing a sustained note, human voice sounds aren't going to be regularly repeating. That means you can't really declare something as the fundamental frequency with everything else being a series of harmonics.

Instead, it makes more sense to think of voice in the context of the continuous spectrum. If you do that you will see most of the signal being in the few 100 Hz range. The phone company long ago figured out what part of the overall spectrum they needed to transmit for voice to sound reasonable at the other end.

If you keep only from about 50 Hz to 3 kHz, then the voice will sound quite good at the other end and individual people can be identified. The fricative sounds, like "s", contain higher frequencies, but we are quite capable of understanding voice limited to 3 kHz. You can get away with making low end cutoff higher, like just under 100 Hz, but the extra 10s of Hz are little burden to carry. In other words, whether the bandwidth is 2.90 kHz or 2.95 kHz makes little difference to cost of transmission.

If you just want understandable voice, not necessarily good quality voice, then you can cut off the high end even lower. Most of the information is below 1 kHz, but the result won't sound "good" if you filter off everything above that. It will sound "mushy" and a bit like someone is talking thru a tunnel. If you do that, it helps to use a male voice since more of the information is in the lower frequecies.

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Human voices tend to average around middle C - male voices average an octave below this and female voices an octave above. Middle C is 261.6Hz.

If you have an amplitude-time graph the way to measure the frequencies contained in it is to Fourier transform it. This gives you a plot of amplitude against frequency. If you take some reasonable clear signal, like a singer singing a constant note, you should see a clear fundamental frequency and overtones. For some random bit of speech you'll most likely get a broad range of frequencies.

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Specifying the average human voice frequency to 4 digits is absurd. Doing so is wrong because you are claiming details you can't possibly know. –  Olin Lathrop Sep 6 '13 at 18:42
    
Olin, he specified middle c to four figures, but he states that "voices tend to average around middle C". Hardly a claim to four figure accuracy for the pitch of human speaking. –  dmckee Sep 6 '13 at 19:14
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As Olin Lathrop pointed out, for speech recognition (and indivitual person recognition) the necessary frequency range of the signal must stretch to about 3000 Hz. For instance, the distinction between the various vowels of language is in the higher harmonics of the speech sound.

According to the Wikipedia article about voice frequency:
"The voiced speech of a typical adult male will have a fundamental frequency from 85 to 180 Hz, and that of a typical adult female from 165 to 255 Hz." That is, the frequency ranges (of the fundamental frequency) are about an octave apart, for males and females.

As stated by Olin Lathrop, in the case of speech the fundamental frequency is not necessary for good recognition.

For decades the microphones used in telephone sets (carbon microphones) were of a type that is sensitive from about 300Hz and upwards. That is, those telephone microphones never picked up the fundamental frequency, only 300 Hz and higher.

Incidentally, no doubt the speaker of a telephone can only produce a very weak low frequency sound, and again, that doesn't affect recognition of speech.

For singing, especially in the case of trained singers, full appreciation requires pretty much the hifi quality standard. For the singing voice, a cut-off above 3000 Hz will make it sound numb and impoverished.

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Actually, there may well be typo in the numbers provided by that 'voice frequency' Wikipedia article. A range of 165 to 255 Hz for typical adult female voice (fundamental frequency) looks odd. Quite possibly it's 165 to 355 Hz. Anyway, these numbers are quite irrelevant, so it's not surprising there are no sources for them. –  Cleonis Sep 7 '13 at 8:16
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