Biomedical Engineering Reference
In-Depth Information
x
1
(n)
x
w
10
y
x
(n)
Σ
y
w
10
x
L
w
1 −
1
y
y
(n)
Σ
x
M
(n)
y
z
(n)
Σ
z
ML
w
−
FIgURE 3.2:
The topology of the linear filter designed for BMIs in the case of the 3D reaching task.
x
i
(
n
) are the bin counts input from the
i
ith neuron (total
M
neurons) at time instance
n
, and
z
-1
denotes
a discrete time delay operator.
y
c
(
n
) is the hand position in the
c
coordinate.
w
c
ij
is a weight on
x
i
(
n
−
j
)
for
y
c
(
n
), and
L
is the number of taps.
ferences will be in the number of parameters, and in the way, the parameters
w
ij
of the model are
computed from the data.
For the MIMO case, the weight matrix in the Wiener filter system is estimated by
w
Wiener
=
−1
R
P
(3.10)
R
is the correlation matrix of neural spike inputs with the dimension of (
L
⋅
M
)×(
L
⋅
M
),
r
r
r
11
12
1
M
r
r
r
,
21
22
2
M
R
=
r
r
r
(3.11)
M
1
M
2
MM
where
r
ij
is the
L
×
L
cross-correlation matrix between neurons
i
and
j
(
i
≠
j
), and
r
ii
is the
L
×
L
auto-
correlation matrix of neuron
i
.
P
is the (
L
⋅
M
)×
C
cross-correlation matrix between the neuronal bin
count and hand position as
