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For speech signals, do the harmonics have a constant bandwidth above some threshold (arbitrarily, -6 dB dropoffs)? Or does this bandwidth decrease with the upper harmonics? If this is not known, how can it be measured? (I could imagine one way would be find -6 dB dB points around peaks of a given frame of samples).

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  • $\begingroup$ i've always thunk i knew something about audio (of which speech signals fall into that category) and that i knew something about what electrical engineers call "Q", but what is the "Q [of a] harmonic"? "Q" was originally an attribute or property of a (normally resonant) 2nd-order analog filter. now that can be related to IIR digital filters ("biquads") and it can even be related to frequency responses and, then, impulse responses. but you have a signal with harmonics. the harmonics have frequency, amplitude, and phase. what other attributes are there for the harmonics? $\endgroup$ – robert bristow-johnson Jul 8 '15 at 0:20
  • $\begingroup$ or do you mean the resonant cavity of one's vocal tract and mouth? is that what you mean regarding Q? $\endgroup$ – robert bristow-johnson Jul 8 '15 at 0:21
  • $\begingroup$ looking at a spectrogram of a sample of speech, there are (mostly evenly) spaced-apart streaks. even with very high N FFT, these streaks, the harmonics some associated bandwidth, they are hardly ever (in natural sounds at least) pure sinusoids. by Q here I mean the ratio of the center frequency of the harmonic to its bandwidth. $\endgroup$ – panthyon Jul 8 '15 at 0:28
  • $\begingroup$ perhaps Q is not an appropriate choice here, but the bandwidth, above some arbitrary threshold, of the harmonics. not well defined. $\endgroup$ – panthyon Jul 8 '15 at 0:29
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    $\begingroup$ okay, with MATLAB or the analysis program of your choice, take your 4096-sample Hann window, append it with zeros on both sides (or, since the DFT periodically extends the input data, it's okay to append it with zeros on one side) and FFT that. (perhaps the FFT is 8192 or 16384 points.) now you will see a spectrum that will have discrete frequency bins that represent content for frequencies spaced by $\frac{f_\text{s}}{N}$ where $N$ is the number of FFT points. see how many points to the left and right of the peak that it takes to get down 3 dB each side of the peak. then you have a bandwith. $\endgroup$ – robert bristow-johnson Jul 9 '15 at 20:47
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If the process that creates a spectrogram includes the use of a windowing function, then the artifacts of that windowing will have a nonzero bandwidth associated with that particular window function (including its length).

If a signal is modulated, then it will have a non-zero bandwidth. Any tiny variations in the mouth cavity shape or in the amplitude of the glottal closures or in the time period between glottal closures of voiced speech could be a cause of modulation of the harmonics. These factors seem unlikely to be a fixed constant for all humans at all times. Which might lead one to doubt a hypothesis of fixed bandwidth.

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    $\begingroup$ even if the signal is not modulated, analysis with a window will smear out the discrete harmonic frequencies into something resembling having a non-zero bandwidth. but that bandwidth depends on the analysis window. $\endgroup$ – robert bristow-johnson Jul 9 '15 at 20:48

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