Biomedical Engineering Reference
In-Depth Information
FIgURE 4.1:
Histogram of the magnitudes of weights over all the coordinates of hand position (HP),
trained by weight decay (solid line), and NMLS (dotted line).
A generalized feedforward filter (GFF) provides a signal processing framework to incorpo-
rate both finite (FIR) and infinite impulse response (IIR) characteristics into a single linear system
by using a local feedback structure in the delay line as a generalized delay operator [
19
]. As shown
in Figure
4.2
, an input signal is delayed at each tap by a delay operator defined by specific transfer
function
G
(
z
). Note that when
G
(
z
) =
z
−1
, it becomes an FIR filter. The transfer function of an
overall system
H
(
z
) is stable when
G
(
z
) is stable because
K
å
0
k
=
( )
=
(4.20)
H z
( )
w
G z
( )
k
k
where
K
is the number of taps. It has been shown that a GFF can provide trivial stability checks if
G
(
z
) is a first- or second-order polynomial in
z
, and easy adaptation while decoupling the memory
TaBlE 4.1:
Comparison of testing performance for weight decay and NLMS
NlMS
wEIghT dECay
Testing a correlation
coefficient for reaching task
0.75 ± 0.20
0. 77 ± 0.18
