Digital Signal Processing Reference
In-Depth Information
tempo range deduced from the dance style can be enforced on the quarter-note tempo
detection. This method is very effective in eliminating octave errors.
The envelopes or detection functions of six non-linear frequency bands are fed into
comb filters as first introduced in [
5
] to detect the fastest, i.e., Tatum tempo [
19
,
75
]
by highest output energy. The comb-filter bank used in the ongoing is a specialised
version. From this information features are derived that describe the distribution of
resonances throughout the musical piece of analysis. These allow for the automatic
decision upon duple or triple metre, and ballroom dance style classes, which assist the
tempo detection algorithm. The tempo is from now on denoted by
and is specified
by a frequency with the unit BPM. The subscript IOI indicates that it is given as IOI
period in frames.
Let us next look at the comb filters in detail. It basically adds the signal itself to a
delayed version of the signal and is characterised by two parameters: the 'delay'
d
or
period, being the reciprocal value of the filter's resonance frequency, and the gain
θ
α
.
For tempo detection IIR comb filters are used with the output
y
(
k
)
in the discrete
time domain:
y
(
k
)
=
(
1
−
α)
·
s
(
k
)
+
α
·
y
(
k
−
d
)
(11.15)
The according transfer function
H
(
z
)
in the
z
-domain is:
1
−
α
H
(
z
)
=
(11.16)
z
−
d
1
−
α
·
H
is a crucial
factor to achieve best tempo detection. In [
5
] it is suggested to use a constant half-
energy time by using variable gain
(
z
)
is depicted in Fig.
11.6
for two exemplary gains
α
. Optimising
α
depending on
d
. This was, however, not observed
ideal in the oncoming experiments, and a fixed value for
α
is thus preferred. As small
temporary tempo drifts within a musical piece have to be assumed, the gain
α
α
→
1
Fig. 11.6
Frequency
responses of IIR comb fil-
ters for the gains
0
alpha =
α
=
0
.
8and
0.4
α
=
0
.
4 set for 100 BPM
−10
alpha =
0.8
−20
0
50
100
150
200
250
300
350
400
450
tempo [BPM]
