I read* that one reason that f0 varies over time owes to the quasi-periodic nature of vocal chord vibrations.
But what does f0 variation over time have to do with the quasi-periodicity of the signal?
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Sign up to join this communityI read* that one reason that f0 varies over time owes to the quasi-periodic nature of vocal chord vibrations.
But what does f0 variation over time have to do with the quasi-periodicity of the signal?
Well, this is really a basic mathematics or physics question. The frequency of a sound is "F0" if and only if "1/F0" is the smallest possible period of time for which
pressure (t) = pressure(t+1/F0)
for each moment of time "t". To be able to define the frequency means to define the periodicity of the pressure waves (sound are oscillations), and the frequency (in Hz) is the inverse of the periodicity (in seconds). For example, a tone with the frequency 500 Hz is periodic and the oscillating pressure gets repeated every 1/500=0.002 second.
However, no such exact periodicity exists for the human voice – which also means that "F0" isn't quite well-defined, either. The vibrations of the vocal cord are complicated and not periodic. They are close to periodic ones but not quite periodic: they are "quasi-periodic". It means that some frequency "dominates" but it cannot be determined exactly. The vibrations of the vocal cord are aperiodic because different points of the vocal cord vibrate independently and the vibrations can't be divided to simple harmonics because they affect each other, due to "nonlinearities" of the equations governing the vocal cord.
Ideally, one could consider sounds that are periodic, with the periodicity "1/F0". Such sounds may be written as "Fourier sums" (Fourier series, Fourier expansions) over the frequency "F0" and the "higher harmonics" such as "2*F0", "3*F0", and so on. Each of these higher harmonics would have some coefficient which would describe the "color" of the sound.
However, the human voice isn't quite periodic so the Fourier series aren't enough. We need a full-fledged "Fourier transform" in which all frequencies, and not just a multiple of "F0", are represented. Some frequencies around "F0" (and partly its multiples) make higher contributions but the other frequencies can't be completely neglected.