Databases Reference
In-Depth Information
and
⎡
⎤
c
10
c
20
c
30
.
c
M
0
⎣
⎦
S
=
(17)
The elements
c
ij
are estimated as
n
0
+
N
c
ij
=
y
n
−
i
y
n
−
j
(18)
n
=
n
0
+
1
Notice that we no longer assume that the values of
y
n
outside of the segment under consider-
ation are zero. This means that in calculating the
C
matrix for a particular segment, we use
samples from previous segments. This method of computing the filter coefficients is called the
covariance method
.
The
C
matrix is symmetric but no longer Toeplitz, so we can't use the Levinson-Durbin
recursion to solve for the filter coefficients. The equations are generally solved using a tech-
nique called the
Cholesky decomposition
. We will not describe the solution technique here.
(You can find it in most texts on numerical techniques; an especially good source is [
182
].) For
an in-depth study of the relationship between the Cholesky decomposition and the reflection
coefficients, see [
232
].
The LPC-10 algorithm uses the covariance method to obtain the reflection coefficients.
It also uses the PARCOR coefficients to update the voicing decision. In general, for voiced
signals the first two PARCOR coefficients have values close to one. Therefore, if both the first
two PARCOR coefficients have very small values, the algorithm sets the voicing decision to
unvoiced.
Transmitting the Parameters
Once the various parameters have been obtained, they need to be coded and transmitted to
the receiver. There are a variety of ways this can be done. Let us look at how the LPC-10
algorithm handles this task.
The parameters that need to be transmitted include the voicing decision, the pitch period,
and the vocal tract filter parameters. One bit suffices to transmit the voicing information. The
pitch is quantized to 1 of 60 different values using a log-companded quantizer. The LPC-10
algorithm uses a 10th-order filter for voiced speech and a 4th-order filter for unvoiced speech.
Thus, we have to send 11 values (10 reflection coefficients and the gain) for voiced speech and
5 for unvoiced speech.
The vocal tract filter is especially sensitive to errors in reflection coefficients that have
magnitudes close to one. As the first few coefficients are most likely to have values close to
one, the LPC-10 algorithm specifies the use of nonuniform quantization for
k
1
and
k
2
.The
nonuniform quantization is implemented by first generating the coefficients
1
+
k
i
g
i
=
(19)
1
−
k
i
