Biomedical Engineering Reference
In-Depth Information
7. Appendix 2:
Quantification of
Signal and Noise
in Timeseries
Consider the time-series, x
i
(t) representing either the signal
of a sensor or the activation of a region of interest (ROI)
for the ith single trial. For example,
x
i
(t)could be defined
as
x
i
(
t
)
=
ROI
J
i
(r, t)
u
ROI
d
3
r, with J
i
(r, t)the instantaneous
estimate for the current density vector at time t and trial (i) and
ˆ
· ˆ
u
ROI
the direction of the current density vector at the maximum
(modulus) of the MFT activation. A quantitative measure of the
signal-to-noise ratio (SNR) can be derived from the ensemble of
single trial timeseries using a conventional SNR estimator
(39)
.
The spatial specificity of the MFT solutions allows such estimates
to be made for relatively small segments of regional activations,
and hence map their evolution across the latency axis. Around
each timeslice t, we define aligned data segments X
i
(t, p)
=
x
i
(t
2
)
consisting of
p
samples. The noise power (NP) and signal power
(SP) and SNR can then be defined using the following equations
(36, 40)
:
p
−
1
p
−
1
−
),
...
, x
i
(t
−
1), x
i
(t), x
i
(t
+
1),
...
, x
i
(t
+
2
N
i
=
1
X
N
i
=
1
X
1
(t, p)
N
2
L
2
−
X
i
(t, p)
X
=
, NP
=
,
p(N
−
1)
1
1
N
NP, SNR
SP
NP
p
X
L
2
−
SP
=
=
For further discussion about these measures and their mean-
ing see
(36, 41)
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