Database Reference
In-Depth Information
windows. The size of the Hamming window is taken to be 10 ms. This descriptor is
calculated using the following equation [
220
]:
exp
nk
2
N
N
−
1
)=
∑
(
,
(
+
)
(
)
−
(
)
S
l
k
s
n
lM
w
n
j
(7.46)
n
=
0
where
s
is the short time Fourier transform
coefficient,
N
is the size of the transformed signal,
k
is the frequency bin index,
l
is
the time audio frame index,
w
(
n
)
is the original audio signal,
S
(
l
,
k
)
is the analysis window function of length
lw
and
M
is the hop size. The short time Fourier transform
S
(
n
)
needs to be normalized
by a factor of
N
in order to preserve Parseval's Theorem and since ASE represents
only the power spectrum, therefore we can estimate the ASE descriptor as follows:
(
l
,
k
)
1
ʱ
·
2
ASE
(
l
,
k
)=
N
|
S
(
l
,
k
)
|
(7.47)
where
is the window normalization factor. The number of frequency bins can
be varied based on the octave resolution required. One bin is reserved for power
between 0 and 62.5 Hz, while another one is reserved for power between 8 kHz and
Nyquist rate. With 1/8 of octave resolution the frequencies in the middle are divided
into eight bins, thus providing a spectrum envelope consisting of ten bins.
The ASC descriptor represents the center of gravity of the power spectrum. This
is calculated by adding the energy in each frequency bin in the FFT spectrum and
dividing it by the total energy in the frame, as shown below:
ʱ
K
1
k
=
0
k
−
2
·|
ASE
(
l
,
k
)
|
ASC
(
l
)=
(7.48)
K
1
k
=
0
|
−
2
(
,
)
|
ASE
l
k
where
k
is the frequency bin's index. The descriptor shows which frequencies are
dominant in the spectrum.
The ASF descriptor represents the overall tonal component in the power spectrum
of the audio signal. It is calculated by calculating the geometric mean of the audio
frame and dividing it by the arithmetic mean of the audio frame, as shown by the
equation:
K
−
1
k
=
0
|
2
N
ASE
(
l
,
k
)
|
ASF
(
l
)=
(7.49)
K
−
1
k
=
0
|
1
N
2
ASE
(
l
,
k
)
|
where
k
is the frequency bin's index and
N
is the size of the short time Fourier
transform window.
Search WWH ::
Custom Search