Digital Signal Processing Reference
In-Depth Information
EFR weighting
This weighting function is used in the GSM Enhanced Full Rate standard
(EFR) [10]. The weights are calculated as follows:
1
.
547
450
3
.
347
−
d
n
for
d
n
≤
450
w
n
=
(5.62)
0
.
8
1050
(d
n
1
.
8
−
−
450
)
otherwise
where
d
n
=
f
n
+
1
−
f
n
−
1
(5.63)
and
f
n
is the
n
th
LSF,
f
0
=
0and
f
11
=
4000.
LSF inverse distance
This method is based on the principle that the peaks in the LPC filter are
located where two consecutive LSFs are close to each other. The weighting is
given by:
4000
4000
( f
n
+
1
w
n
=
f
n
−
1
)
+
(5.64)
( f
n
−
−
f
n
)
Group Delays
This weighting is based on the group delay of the LPC filter and is defined as
[11]:
u( f
n
)
D
n
D
max
1
.
375
≤
D
n
≤
D
max
w
n
=
(5.65)
D
n
u( f
n
)
√
1
.
375
D
max
D
n
<
1
.
375
where
1
f
n
<
1000
u( f
n
)
=
0
.
5
3000
(f
n
(5.66)
1
−
−
1000
)
1000
≤
f
n
≤
4000
D
n
is the group delay of the LPC filter at the frequency
f
n
in milliseconds
whilst
D
max
is the maximum group delay, experimentally found to be around
20ms.
The group delays of the filter are larger at the formant frequencies, therefore
the weighting will be higher for these frequencies. The factor
u(f
n
)
simply
reduces the weights for the higher frequencies to take into account the
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