Digital Signal Processing Reference
In-Depth Information
Fig. 11.2
Gains of a drum
(
top
) and harmonic component
(
bottom
) from David Bowie
and Mick Jagger's “
Dancing
In The Street
”, and their
convolution with a linear
decay function
Gains
Convolution
Gains
Convolution
with a linear decay function of height 1 and length 200 ms. Percussiveness is then the
(Pearson product-moment) correlation coefficient of the convolution and the original
vector
g
. This is illustrated in Fig.
11.2
.
Next,
Periodicity
[
44
] models drum patterns often being periodic in intervals
corresponding to a musical piece's tempo. Autocorrelation values normalised by
mean and variance of
g
are computed for delays corresponding to tempi of 30-
240 BPM, at intervals of 5 BPM. The maximum of these coefficients is defined as
the periodicity.
Finally,
average peak length
and
peak fluctuation
are added, where a peak is 'any
area' of
g
that is above a threshold of 20 % of the maximum of
g
. Formally, a peak
of length
l
is a set of consecutive indices
{
i
,
i
+
1
,...,
i
+
l
−
1
}⊆{
1
,...,
M
}
such
that [
21
]:
g
i
,
g
i
+
1
,...,
g
i
+
l
−
1
≥
0
.
2
·
max
{
g
i
}
.
(11.6)
Once the peaks in
g
are located, the average peak length is given by the sample
mean of the peak lengths, and the peak fluctuation by their sample standard deviation
