Fig. 6. Block diagram of ANC system with feedback.
Fig. 7. ANC with acoustic feedback neutralization.
1) Feedback Neutralization: The simplest approach to
solving the feedback problem is to use a separate feedback
cancellation, or “neutralization,” filter within the controller,
which is exactly the same technique as used in acoustic echo
cancellation [43]. This electrical model of the feedback
path is driven by the secondary signal, and its output
is subtracted from the reference sensor signal [44]. A
duct-acoustic ANC system using the FXLMS algorithm
with feedback neutralization is illustrated in Fig. 7. The
feedback component of the reference microphone signal
is canceled electronically using a feedback neutralization
filter
which models the feedback path
Since the primary noise is highly correlated with the
antinoise, the adaptation of the feedback neutralization filter
must be inhibited when the ANC system is in operation,
similar to adaptive echo cancellation during periods of
double talk. Thus, feedback neutralization is achieved, in
effect, by using an offline adaptive method for determining
the transfer function of the feedback path. The models
and can be estimated simultaneously by using the
offline modeling technique [4].
2) Adaptive IIR Filter: Equation (14) shows that when
feedback is present, the optimal solution of the adaptive
filter is generally an IIR function with poles and zeros. This
rational function can be approximated by an FIR function
of sufficient order, but a smaller step size
then has to
be used for stability reasons. The poles of an IIR filter
make it possible to obtain well-matched characteristics with
a lower order structure, thus requiring fewer arithmetic
Fig. 8. ANC system using the filtered-U recursive LMS algo-
rithm.
operations [41]. However, the disadvantages of adaptive
IIR filters are: 1) IIR filters are not unconditionally stable
because of the possibility that some pole(s) of the filter
will move outside of the unit circle during the adaptive
process, causing instability; 2) the adaptation may converge
to a local minimum because the MSE function of adaptive
IIR filters is generally nonquadratic; and 3) IIR adaptive
algorithms can have a relatively slow convergence rate
in comparison with that of FIR filters. A comprehensive
discussion of adaptive IIR filters can be found in the
literature [45], [46].
A block diagram of an adaptive IIR ANC system [47]
is illustrated in Fig. 8. The output signal of the IIR filter
is computed as
(16)
where
is the weight
vector of
is the reference signal vector,
is the weight vector of and
is the output signal vector delayed by one sample.
Many algorithms can be employed to find the optimal set
of coefficients
and to minimize the error signal
In 1976, Feintuch [48] suggested that the recursion based
on the old output gradients is negligible. Based on this
suggestion, the “filtered-U recursive LMS algorithm” [49]
for ANC is derived as [4]
(17)
(18)
where
is the filtered version
of the canceling signal vector at time
In practice, it
is reasonable to use a higher order for
than for
[50]. Real-time experiments have been conducted to test
the system performance for various reference microphone
locations, error microphone locations, and different time-
varying sources, such as a centrifugal fan and diesel engine
[51].
Given the complexities associated with the pole-zero
structure of
and one cannot predict the
values to which
and will converge. Also, global
convergence and stability of the filtered-U recursive LMS
948 PROCEEDINGS OF THE IEEE, VOL. 87, NO. 6, JUNE 1999
Authorized licensed use limited to: UNIVERSITY OF SOUTHAMPTON. Downloaded on August 6, 2009 at 09:24 from IEEE Xplore. Restrictions apply.
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