Information Technology Reference
In-Depth Information
()
(1)
X
i
t
,
i
=
1
"
,
r
where
r
is the number of frames into which the signal has been divided.
The next step consists in sampling any frame
()
X
i
t
:
()
X
i
t
,
k
=
1
"
,
p
(2)
k
where
p
is the number of samples per frame.
Since each frame
X
i
(
t
) is a windowed stochastic process, any of its samples,
X
i
(
t
k
),
is a random variable, labeled
X
i k
.
Thus, for each audio frame,
X
i
(
t
), the following random vector is obtained:
(3)
[
]
X
=
X
1
"
,
,
X
i
i
ip
This is just the initial information the system uses to calculate all the features de-
scribing frame
X
i
(
t
).
With respect to the aforementioned features, let
(4)
{
}
Γ
=
f
1
"
,
,
f
N
F
be the set that contains all the available features,
N
F
being the number of features.
Any feature
f
k
can be assumed, in the most general case, as a complex function of
p
complex variables:
(5)
p
f
:
C
→
C
k
Since frame
X
i
(
t
) has been shown to be the random-variable vector in Eq. 3, then
any feature
f
k
applied on it,
f
k
(
X
i
), is thus a function of
p
random variables,
f
k
(
X
i1
,...,
X
ip
), and, consequently, a random variable. In order to simplify the notation, the ran-
dom variable,
f
k
(
X
i1
,...,
X
ip
), will be labeled
f
ki
.
Finally, for completing the characterization of the input audio signal, the aforemen-
tioned sequence of processes has to be applied onto all the
r
frames into which the in-
put audio signal has been segmented.
The next step assesses how feature
k
f
describes the input signal. One of the
results that provides the previously described sequence of processes is the random
data vector
[
∈
Γ
]
(6)
f
1
"
,
f
≡
F
k
kr
The elements of this vector are the results obtained when feature
f
k
is applied to
each of the
r
frames into which the input audio signal has been segmented to be proc-
essed. The random vector
F
k
can be characterized for example by estimating its mean
value:
(7)
[]
E
ˆ
F
and its variance:
(8)
[]
2
ˆ
σ
F
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