Digital Signal Processing Reference
In-Depth Information
Fig. 4.1
Scheme of an adap-
tive noise canceler (ANC)
4.2.6 Example: Adaptive Noise Cancelation
The general idea of an adaptive noise canceler (ANC) is depicted in Fig.
4.1
.One
sensor would receive the
primary input
, that works as desired signal
d
(
n
)
in our
(
n
)
, corrupted by
additive uncorrelated noise
v
0
(
n
)
, i.e.,
d
(
n
)
=
s
(
n
)
+
v
0
(
n
),
E
[
s
(
n
)
v
0
(
n
−
i
)
]=
0
∀
i
.
(4.30)
Another sensor provides the
reference input
, which will be the input
x
(
n
)
to the
adaptive filter. This sensor receives a noise
v
1
(
n
)
which is uncorrelated with the
signal
s
(
n
)
,but
correlated
with
v
0
(
n
)
, i.e.,
x
(
n
)
=
v
1
(
n
),
E
[
s
(
n
)
v
1
(
n
−
i
)
]=
0
∀
i
,
E
[
v
0
(
n
)
v
1
(
n
−
i
)
]=
r
(
i
),
(4.31)
(
)
where
r
is an unknown cross correlation for lag
i
. In this way, the adaptive filter will
produce at its output an estimate for the error corrupting the signal on the primary
input,
i
. This estimate can then be subtracted from the primary input, so the
“error signal” is actually the estimate for the signal of interest,
ˆ
v
0
(
n
)
, and so it is the
output of the ANC.
5
As the error signal, this is used to adjust the coefficients of the
adaptive filter. In minimizing the mean square value of the output of the ANC, it ends
up being the best MSE estimate of the signal, since as the reference signal
v
1
(
ˆ
s
(
n
)
n
)
is
only correlated with the noise
v
0
(
remains essentially unaffected.
This can also be interpreted as maximizing the output signal to noise ratio (SNR).
The positioning of the reference sensor is important for the performance of the ANC
in order to satisfy (
4.31
) in the best possible way.
The ANC can be used in many applications [
4
], as adaptive speech enhancement
(listening to speech in the presence of background noise), adaptive line enhance-
ment (detecting a periodic signal in broadband background noise), acoustic echo
cancelation (coupling problems between a loudspeaker and a microphone), line echo
cancelation (impedance mismatch in the analog loop of the telephone network), etc.
In this example we focus on another application which is power line interference
(PLI), usually seen as a combination of sinusoids at 50/60Hz and harmonics. When
n
)
, the signal
s
(
n
)
5
If this subtraction is not done properly (under the control of an adaptive filter) it might lead to an
increase of the output noise power.
