Biomedical Engineering Reference
In-Depth Information
clock cycle back in time, we simply multiply an additional
w
f
T
D
t
−
i
. The general form of the sensitiv-
ity calculation is shown in (
4.35
). Experimentally, we determined that the effect of an input decays
to zero over a window of 20 samples (Figure
4.4
). At each time
t
, the sensitivity of the output with
respect to the input is represented as the sum of the sensitivities over the 20-sample window.
∂
∂
y t
x t
( )
( )
(4.32)
2
T
T
=
D
W W
2
t
1
f
′
(
z
1
1
)
�
0
0
′
2
1
0
f
(
z
)
�
�
D
=
�
�
�
0
�
f
′
(
z
)
0
0
(4.33)
1
∂
∂ −
=
y
( )
t
(4.34)
T
T
T
2
D
D
W W
W
2
t
f
t
−
1
1
x t
(
1
)
∂
∂ −
y
( )
t
∆
( )
∏
(4.35)
2
T
T
T
=
D
D
W
W
W
2
1
t
f
t
−
i
x t
(
∆
i
=
1
Compared to the FIR model, which produces a static measure of sensitivity, the RMLP
produces a time-varying sensitivity that we will now use to analyze three similar movements from
5
x
10
-3
X
Y
Z
4
3
2
1
0
0
5
10
15
20
∆
FIgURE 4.4:
Sensitivity at time
t
for a typical neuron as a function of Δ.
