Digital Signal Processing Reference
In-Depth Information
to more reliable results if the tempo is sufficiently constant over longer segments. It
will thus be followed in the ongoing. As in the case of onset detection (cf. Sect.
11.2
),
the assumption is made that beats, percussion or note onsets, and other rhythmic
events are marked by a change in signal amplitude in a few non-linear frequency
bands. The starting point thus is the envelopes or the differentials of the envelopes
of six frequency bands, however, without peak picking. The 'detection function' (cf.
Sect.
11.2
)[
57
] will be the envelope, its differential, or any other function related to
perceivable change in the signal
s
.
The beat level tempo we aim at now, can be seen as periodicity in the envelope
can be used here to find the periodicity [
19
,
80
]. The periodic auto-correlation is cal-
culated over a window of 10 s of the envelope function. As in the case of pitch
detection, the index of the ACF's highest peak indicates the strongest periodicity.
However, this strongest periodicity does not necessarily correspond to the periodic-
ity perceived as dominant [
81
], which may be influenced by an interval of preferred
tapping linked to a supposed resonance between the human perceptual and motor
system. Ignoring this fact, however, and using this highest peak as indication of the
beat level tempo can give reasonable results if the music of consideration has strong
beats in the preferred tapping range. Given, however, that multiple frequency bands
were used, their results need to be combined in a meaningful way. A straightforward
approach is the addition of the bands' individual ACFs (cf., e.g., Fig.
11.5
) leading to
the summary ACF (SACF). In the SACF, one then picks the highest peak. Alterna-
tively, one can determine the tempo per band and carry out a majority vote over these
decisions—potentially even weighted according to the type of music. An example
of ACF application is given in [
13
] for tempo and in [
19
] for metre detection.
A related method is the use of a resonant filter bank [
5
]. Such a bank is made up by
resonators tuned to different frequencies or periodicities, respectively. The detection
function is input to all resonators. Then, the total output energy is measured per
resonator. Similar to the ACF approach, the resonator with the highest output energy
best matches the piece's periodicity. Thus, one assumes the beat level tempo to be
its resonance frequency. As stated, this is an incomplete, yet 'working' model of the
considerably more complex human rhythm perception. In fact, most state-of-the-art
(
k
)
acf band 1
acf band 3
acf band 5
acf band 6
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
T [s]
T [s]
T [s]
T [s]
Fig. 11.5
Periodic ACF of band envelope differentials from 10 s of OMD—“
Maid of Orleans
”[
6
]
