Why do envelope extraction before pitch detection? I am referring to this report on pitch estimation. 

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



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


Fig 2
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.