Digital Signal Processing Reference
In-Depth Information
10
10
ARMA(4,1)
and ARMA(3,2)
8
8
ARMA(3,2)
6
6
4
4
2
2
0
0
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
(a)
(b)
Figure 3.29 Two different filters give the same frequency response
order of the numerator polynomial and q is the order of the denominator
polynomial.
3.11.2 Estimating Filter Coefficients
Refer
to
(1.24)
to
(1.26)
for
the
definition
of
the
vector
p ¼½
a
1
;
a
2
; ...;
a
p
;
b
1
; ...;
b
q
which defines the digital filter. We also have another vector
t
z
k
¼½
y
k
1
; ...;
y
k
p
;
u
k
; ...;
u
k
q
. Then we construct an equation representing the
t
. This is exactly the same as the set of overdetermined
simultaneous equations given in Chapter 2 and the solution has the form of (2.35).
Using (2.36) and (2.33), we arrive at the solution for
given data as y
k
¼ z
k
p
p
as
!
1
!
X
N
k
¼
1
z
k
z
X
N
t
k
t
k
p ¼
y
k
z
:
ð
3
:
51
Þ
i
¼
1
There are many methods centred around this solution and they are shown in
Figure 3.29A.
This vector
z
k
can be noisy
(
Σ
k=
1
z
k
z
k
)
t
N
Covariance matrix
t
A noise-free or independent source of the
z
k
-like vector is the
key
Figure 3.29A There are many methods centred around solution (3.51)
Search WWH ::
Custom Search