Digital Signal Processing Reference
In-Depth Information
Fig. 3.25 Noise reduction
using an adaptive filter
^
x
(
n
)
Adaptive
filter
z
−1
y
(
n
)
d
(
n
)
3.5.8 Application of Adaptive Filtering to Noise Reduction
in Narrow-Band Signals
For noise removal in narrowband signals of unknown frequency one can use
adaptive LMS filters. In such applications one can set the desired signal d(n)tobe
equal to the observed signal (d(n) = y(n)), as shown in Fig.
3.25
. Note that with
this arrangement: i) the filter operates only on previous samples of the signal (not
the current one) and ii) the filter coefficients are adapted until the current output
from the filter matches the current observed sample as closely as possible. Now
ideally the desired signal should not be derived from the (noisy) observed signal
but from a noise free version of the observed signal. However, if the filter coef-
ficients are forced to adapt slowly, the filter will be unable to adapt to the rapid
fluctuations of the noise component of the observation—they will adapt mostly to
the noise-free version of the observed signal. The adaptive filter therefore func-
tions reasonably effectively. The arrangement is illustrated in Fig.
3.26
which
shows adaptive noise reduction for a sinusoid with unknown frequency.
{
x
(
k
)}
{
x
(
k
)+
n
(
k
)}
2
2
0
0
−2
−2
0
5
10
0
5
10
Estimated {
x
(
k
)},
μ
=.00001
Estimated {
x
(
k
)},
μ
=.002
2
2
0
0
−2
−2
0
5
10
0
5
10
Estimated {
x
(
k
)},
μ
=.01
2
0.2
0
0.1
−2
0
0
5
10
0
0.005
0.01
μ
Fig. 3.26
Noise reduction for a sinusoid of unknown frequency using a 100-taps adaptive FIR filter
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