Biomedical Engineering Reference
In-Depth Information
e
k
+
(Estimated signal)
Σ
s
k
=
x
k
+
k
(Corrupted signal)
−
Digital filter
r
k
k
(Noise)
(Noise estimate)
LMS
algorithm
FIGURE 2.22
Adaptive filter with coecients determined using the least mean squares
algorithm.
+
+
+
N
Σ
k
=
w
k
(
i
)
r
k
−
i
i
=1
w
k
(1)
w
k
(2)
w
k
(3)
w
k
(
N
)
r
k
z
−
1
z
−
1
FIGURE 2.23
Structure of an
N
-point FIR filter with
N
-filter coecients.
is correlated with
r
k
. The Wiener filter then produces an optimal estimate
of the correlated part, which is subtracted from
s
k
. In adaptive filters, the
correlated component is the noise to be removed.
For an FIR filter structure (Figure 2.23) with
N
filter coecients, the dif-
ference between the output of the Wiener filter and the correlated signal is
given by
N
w
T
r
k
e
k
=
s
k
−
w
i
r
k−i
=
s
k
−
(2.167)
i
=1
where
w
=
w
1
,w
2
,...,w
N
is the vector of filter coecients (sometimes known
as weights) and
r
=
r
k
+1
,r
k
,...,r
N
is the reference noise signal. The square
Search WWH ::
Custom Search