Biomedical Engineering Reference
In-Depth Information
3.3.2.3.1 dDTF
In order to distinguish direct from indirect flows direct directed
transfer function (dDTF) was introduced [Korzeniewska et al., 2003]. The dDTF is
defined as a multiplication of a modified DTF (
F
ij
(
) by partial coherence (
C
ij
(
).
The modification of DTF concerned normalization of the function in such a way as to
make the denominator independent of frequency. The dDTF (χ
ij
f
)
f
)
(
f
)
) showing direct
propagation from channel
j
to
i
is defined as:
χ
ij
(
F
ij
(
κ
ij
(
)=
)
)
f
f
f
(3.34)
2
|
H
ij
(
f
)
|
F
ij
(
f
)=
(3.35)
∑
f
∑
k
m
=
1
|
2
H
im
(
f
)
|
has a nonzero value when both functions
F
ij
(
and κ
ij
(
χ
ij
(
f
)
f
)
f
)
are nonzero; in
that case there exists a causal relation between channels
j
i
and that relation is
direct. The DTF and dDTF for the same simulation scheme are presented in Figure
3.2. One can see that dDTF shows only the direct flows, whereas in the case of DTF
→
FIGURE 3.2:
a) In each box DTF as a function of frequency, on the diagonal
power spectra; propagation from channels labeled above to the channels labeled at
the left of the picture; b) dDTF is shown using the same convention as in a); c)
simulation scheme; d) signals used in the simulation.
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