User`s guide

Autocorrelation LPC
5-32
Algorithm The Autocorrelation LPC block computes the least-squares solution to
where indicates the 2-norm and
Solving the least-squares problem via the normal equations
leads to the system of equations
where r =[r
1
r
2
r
3
… r
n+1
]
T
is an autocorrelation estimate for u computed
using the Autocorrelation block, and * indicates the complex conjugate
transpose. The normal equations are solved in O(n
2
) operations by the
Levinson-Durbin block.
Ua
˜
b–
a
˜
ℜ
n
∈
min
⋅
U
u
1
0 L 0
u
2
u
1
OM
M u
2
O 0
MMOu
1
MMMu
2
MMMM
u
M
MM M
0 OM M
MOOM
0 L 0 u
M
, a
˜
a
2
M
a
n 1+
, b
u
2
u
3
M
u
M
0
M
0
===
U
*
Ua
˜
U
*
b=
r
1
r
2
*
L r
n
*
r
2
r
1
OM
MOOr
2
*
r
n
L r
2
r
1
a
2
a
3
M
a
n 1+
r
2
–
r
3
–
M
r
n 1+
–
=