Digital Signal Processing Reference
In-Depth Information
Fig. 11.1
Spectra of a drum
(
top
) and harmonic component
(
bottom
) from David Bowie
and Mick Jagger's “
Dancing
In The Street
”, and their
convolution with a Gaussian
function
Spectrum
Convolution
Spectrum
Convolution
a
1
a
2
e
−
as
(
f
2
−
f
1
)
−
e
−
bs
(
f
2
−
f
1
)
d
(
f
1
,
f
2
,
a
1
,
a
2
)
=
(11.4)
0
.
24
with
a
19
.
Then, spectral dissonance of
x
is defined as the sum of pairwise dissonances of
all its components:
=
3
.
5,
b
=
5
.
75
and
s
=
0
.
021
f
1
+
N
i
−
1
(
f
j
,
f
i
,
x
j
,
x
i
),
d
(11.5)
i
=
1
j
=
1
where
f
i
is the frequency corresponding to index
i
in the spectral vector.
Further, temporal features are calculated from the gains vectors. Per gains vector
g
sample standard deviation is extracted.
Further,
Percussiveness
[
47
] measures how accurately
g
can be modelled using
instantaneous attacks and linear decays resembling the structure of typical drum
patterns. Its computation is similar to the one applied to spectral vectors for the
calculation of noise-likeness. The local maxima of
g
are determined and convolved
=
(
g
1
,...,
g
M
)
