Biomedical Engineering Reference
In-Depth Information
G
xx
(
f
)
Input
G
xx
(
f
)
f
f
0
0
q (
f
)
System
H
(
f
)
2
f
f
0
0
q
xy
(
f
)
Output
G
yy
(
f
)
G
xy
(
f
)
f
f
0
0
(a)
(b)
FIGURE 17.5
:
Input/output spectral relationships for linear systems. Traces in column (a) are
autospectra while traces in column (b) are cross-spectra
With some algebraic manipulation, (17.14) can be obtained.
=
H
(
f
)
2
G
yy
(
f
)
G
xx
(
f
)
G
xy
(
f
)
=
H
(
f
)
G
xx
(
f
)
(17.14)
The complex conjugation of the lower equation yields (17.15).
G
xy
(
f
)
H
∗
(
f
)
G
xx
(
f
)
=
G
yx
(
f
)
=
(17.15)
where
G
xy
(
f
)
e
j
θ
xy
(
f
)
G
xy
(
f
)
=
=
H
(
f
)
e
j
φ
(
f
)
H
∗
(
f
)
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