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I am referring to this report on pitch estimation.

The author does envelope extraction using Hilbert transform before applying AMDF.

enter image description here

What is the advantage of doing that?

Is speech a narrowband or wideband signal? I read somewhere that hilbert envelope extraction works better for narrowband signals.

When I extracted envelope of a speech signal using Hilbert transform, in some places the envelope was almost the same as the original waveform(Figure 1), whereas in other places it tracked the upper portions of waveforms (Figure 2).

Red curve is the Hilbert envelope, blue curve is the speech waveform.

Fig 1 enter image description here

Fig 2 enter image description here

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My guess is that the Hilbert Transform is a pre-processing step which attempts to make the actual pitch detection stage (AMDF, in this case) more robust.

The basic reasoning is this: pitch detection of speech is made more difficult by the time-varying spectral characteristics of the signal. On the other hand, pitch detection of an impulse train is easy: just count the number of samples between each pulse (or look for the first peak of the auto-correlation function/the first dip of the AMDF etc). Pre-processing the speech signal to make it more pulse-like therefore improves the results.

In your diagrams, the Hilbert transform does make the speech pulses more impulsive, though I think that other pre-processing steps (e.g. inverse-filtering by the estimated spectral envelope) is likely to yield better results.

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  • $\begingroup$ Why does Hilbert envelope behave differently in the two figures? $\endgroup$ – user13107 Aug 20 '13 at 10:01
  • $\begingroup$ I think the envelope is behaving the same, but the plots look different because there's a DC offset in the first signal $\endgroup$ – Speedy Aug 20 '13 at 14:49
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In a generic 1st order resonant system, energy is usually continually being exchanged between 2 quantities, such as displacement vs. momentum (etc.), with the combined energy changing at a much slower rate. The Hilbert transformer, after the bandpass, is trying to estimate one quantity (not being measured) from the other (say local air pressure, or displacement of a resonator surface) that is actually measured. If the energy of the sum of the two varying quantities stays about the same over time, then there might be energy at that frequency worth being measured. Otherwise it might be just a measurement transient having not much to do with some resonant happening at that frequency.

Vocalizations usually involve several different vocal tract resonances. It's usually easier to try to detect and/or measure each potential resonance separately when trying to characterize what's going on with a mix of multiple simultaneous energy exchange systems, than to try and solve for the entire mix all at once.

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  • $\begingroup$ I didn't get it, what is displacement and momentum in a speech signal? Also what is the disadvantage in directly doing AMDF without doing envelope extraction? $\endgroup$ – user13107 Aug 20 '13 at 1:45
  • $\begingroup$ i don't see a particularly good reason to put in an envelope follower there, if the purpose is to measure the period of the speech waveform. heck, i don't even see why doing all this bandsplitting is helpful for measuring the period of a monophonic speech waveform. $\endgroup$ – robert bristow-johnson Aug 20 '13 at 2:44
  • $\begingroup$ @robertbristow-johnson they are doing multipitch estimation, perhaps that's why .. $\endgroup$ – user13107 Aug 20 '13 at 9:58
  • $\begingroup$ @user13107 - For an acoustic signal you could consider the exchange relationship to be between volume velocity and pressure of the air. Specific to this case, we could be looking at displacement and momentum in the microphone diaphragm (projected as a voltage) as Hotpaw suggests. I think this answer could be extended to any cyclic relationship between potential & kinetic energy. $\endgroup$ – Speedy Aug 20 '13 at 15:12
  • $\begingroup$ @rbj : The bandsplitting can help find those overtones with vibrato (likely vocal) from less modulated overtones (likely backing instrumental or fan hum). Then the selected overtones can be used for vocal pitch estimation. $\endgroup$ – hotpaw2 Aug 21 '13 at 0:33

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