How to calculate protrusion value for pitch detection project?

After getting the frequency domain data, we
should find out the magnitude of local peak.
However, not every local peak is important. The
more protrusive the local peak is, the more
important it is. Usually, the small protrusion is
caused by the noise signal. Therefore, we
calculate the protrusion for every local peak and
set a threshold to determine which local peak
should be ignored.

protrusion = Va / Max(Vb, Vc)

where A V is the peak magnitude, are the
troughs magnitudes on both sides of the peak. If
we directly calculate the peak’s protrusion value,
we will get some inaccurate results like Fig. 1.

The little protuberance C, makes C’ become a
trough, and the C’ may cause the protrusion of A
not high enough to pass the threshold. For that
reason, before calculating the protrusion, we
apply a mean filter to all frequency samples to
smooth this kind of protuberance. For guitar,
1.25 is a suitable value for the threshold.

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