Digital Signal Processing Reference
In-Depth Information
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
x
s
s
dom
s
cad
c
c
dom
c
cad
p
maj
p
maj
,
dom
p
maj
,
cad
p
min
p
min
,
dom
p
min
,
cad
CHROMA
scale
scale dom
scale cad
chords
chords dom
chords cad
PTR maj
PTR maj dom
PTR maj cad
PTR min
PTR min dom
PTR min cad
v
=
≡
(11.32)
In a data-driven approach, a higher number of non-correlated, yet information
carrying features can lead to better results. However, focussing on the more infor-
mative ones seems reasonable. To this end, feature space optimisation by exhaustive
group-wise elimination by WA is considered. As opposed to knowledge-based evalu-
ation, data-driven evaluation requires a partitioning into training and test instances—
ten-fold SCV is chosen to this end in the ongoing. This leads to mean values over all
data instances. A comparison with correlation analysis results is therefore possible.
11.4.5 Performance
In the optimisation of parameters and methods, let us follow the chain of processing.
As a first result, Table
11.8
shows key determination with and without tape speed
variation compensation. The CLASSIC and MTV sets seem unaffected. However,
the CHANSON and JAZZ ones containing several recordings first stored on analogue
media show good improvement in WA.
Next is the influence of different filter functions for band-pass filtering of semi-
tones. This is seen in Table
11.9
, where the WA differs most for the CLASSIC set by
a maximum difference of 6.8 % WA. For the other genres, the variation reaches 2.5 %
at maximum. Least effective is the triangle filter. Between the remaining candidates,
the Gaussian filter is preferred in the further results. The reason is its best results on
the KEY-ALL set and the highest number of best WA across the other sets.
We will now take a look at the optimal time window from the beginning of a
piece in Table
11.10
. Lowest WA is observed for the first 30 s over all genres. This
contradicts studies which recommend to focus on the beginning of a piece [
91
,
95
]
under the assumption that the 'home key' is present at the beginning and the key
is easily determined thanks to a gradual addition of more and more instruments
in typical introductions of a piece. Good choices are the longer alternatives of the
first 90 s or the whole piece. Interestingly, the first 90 s lead to higher WA for the
