Biomedical Engineering Reference
In-Depth Information
TABLE 19.2:
Multiple-Input/Output Model Estimates
FUNCTION BEING
NORMALIZED RANDOM
ESTIMATED
ERROR,
ε
√
2[1
xy
(
f
)]
−
γ
xy
(
f
)
γ
ˆ
|
√
n
d
|
γ
xy
(
f
)
xy
(
f
)]
1
/
2
2
[2
−
γ
G
vv
(
f
)
G
yy
(
f
)
2
=
γ
ˆ
xy
(
f
)
|
√
n
d
|
γ
xy
(
f
)
xy
(
f
)]
1
/
2
2
[1
−
γ
H
xy
(
f
)
|
|
|
√
2
n
d
|
γ
xy
(
f
)
xy
(
f
)]
1
/
2
2
[1
−
γ
ˆ
[
ˆ
φ
xy
(
f
)
S
.
D
.
φ
xy
(
f
)]
≈
|
√
2
n
d
|
γ
xy
(
f
)
Equations (19.11) and (19.12) are used to calculate the variance and the normalized
random error of the transfer function, respectively.
1
xy
H
xy
2
2
Var[
H
xy
]
−
γ
≈
(19.11)
2
γ
xy
n
d
SD [
H
xy
]
1
x
y
1
/
2
2
[
H
xy
]
−
γ
H
xy
γ
xy
√
2
n
d
ε
=
≈
(19.12)
Then from (19.12), the normalized random error in the gain factor estimates at frequen-
cies
f
1
and
f
2
will be given by (19.13) and (19.14).
[
H
xy
(
f
1
)
]
10)
1
/
2
(1
−
0
.
ε
=
=
0
.
30
(19.13)
(0
.
32)(10)
[
H
xy
(
f
2
)
]
90)
1
/
2
(1
−
0
.
ε
=
=
0
.
033
(19.14)
(0
.
95)(10)
The phase angle estimate, from the standard deviation (
SD
), is given by (19.15).
1
x
y
1
/
2
2
xy
√
2
n
d
≈
ε
−
γ
H
xy
SD [
˜
γ
φ
xy
]
≈
(19.15)
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