Digital Signal Processing Reference
In-Depth Information
FIGURE 7.2.
Adaptive filter structure for noise cancellation.
FIGURE 7.3.
Adaptive filter structure for system identification.
where
E
() is the expected value. The expected value is generally unknown;
therefore, it is usually approximated with a running average or with the instan-
taneous function itself. Its signal component,
E
(
d
2
), will be unaffected and only
its noise component
E
[(
n
y
)
2
] will be minimized. A more complete discus-
sion is found in Widrow and Stearns [1]. This structure will be further illus-
trated with programming examples using C code.
2.
For system identification.
Figure 7.3 shows an adaptive filter structure that can
be used for system identification or modeling. The same input is to an
unknown system in parallel with an adaptive filter. The error signal
e
is the
difference between the response of the unknown system
d
and the response
of the adaptive filter
y
. This error signal is fed back to the adaptive filter and
is used to update the adaptive filter's coefficients until the overall output
y
-
d
. When this happens, the adaptation process is finished, and
e
approaches
zero. If the unknown system is linear and not time-varying, then after the adap-
tation is complete, the filter's characteristics no longer change. In this scheme,
the adaptive filter models the unknown system. This structure is illustrated
later with three programming examples.
3.
Adaptive predictor.
Figure 7.4 shows an adaptive predictor structure that can
provide an estimate of an input. This structure is illustrated later with a pro-
gramming example.
4.
Additional structures have been implemented, such as:
(a)
Notch with two weights
, which can be used to notch or cancel/reduce a
sinusoidal noise signal. This structure has only two weights or coefficients.
It is shown in Figure 7.5 and is illustrated in Refs. 1, 3, and 4.
(b)
Adaptive channel equalization, used in a modem to reduce channel dis-
tortion resulting from the high speed of data transmission over telephone
channels.
=
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