Berdahl - Acoustic Feedback ...

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Acoustic Feedback Cancellation
For Public Address Systems
Experiments using a personal computer
to implement an adaptive filter
Edgar Berdahl
8/25/05
EE373
Prof. Widrow and Dr. Aaron Eliasib Flores
Table of Contents
1.0 Problem Description.................................................................................................. 3
2.0 Previous Work........................................................................................................... 5
2.1 Adaptive Periodic Noise Canceller (APNC)........................................................... 5
2.2 Feedback Noise Canceller (FBNC) ........................................................................ 5
2.3 Block Methods ...................................................................................................... 6
2.4 Other Methods....................................................................................................... 7
2.4.1 Quasi-Proportional Frequency Shifting ........................................................... 7
2.4.2 Automatic Adjustment Of Notch Filters.......................................................... 7
3.0 Implementation On A Personal Computer ................................................................. 8
3.1 Software ................................................................................................................ 8
3.2 α-LMS .................................................................................................................. 8
3.3 2mic Feedback Canceller....................................................................................... 9
4.0 Experimental Results............................................................................................... 10
4.1 Setup ................................................................................................................... 10
4.2 Loop Transfer Functions...................................................................................... 10
4.3 APNC.................................................................................................................. 11
4.4 FBNC and 2mic................................................................................................... 12
4.5 Effects of OS Latency.......................................................................................... 13
5.0 Sound Examples...................................................................................................... 15
5.1 APNC.................................................................................................................. 15
5.2 FBNC and 2mic................................................................................................... 15
5.3 Convergence........................................................................................................ 16
6.0 References............................................................................................................... 18
2
1.0
Problem Description
People use public address (PA) systems to amplify their voices in various situations (see
Figure 1). In many cases, acoustic paths exist between the speaker device and the person,
who will from here onward be referred to as the
talker
to avoid confusion with the
speaker
device. The sum of the acoustic paths is modeled by the dotted line in Figure 1.
Figure 1. Public address (PA) system with the acoustic feedback path (dotted line)
The block diagram presented in Figure 2 describes the feedback loop inherent in the PA
system more explicitly. Assuming that the elements are not being overdriven, the system
is linear.
H
PA
(f)
represents the transfer function due to the amplifier, while
H
f
(f)
represents the cascade of the speaker, room, and microphone transfer functions.
Figure 2. Block diagram of the feedback loop
PA systems are often plagued by acoustic feedback, which is also sometimes referred to
as howling. This occurs when the signal in the feedback loop grows unboundedly, or at
least until elements of the system begin clipping. Since howling is usually very loud, it is
unpleasant. Here systems for canceling acoustic feedback are investigated.
The Nyquist criterion for stability requires that |
H
PA
(f)H
f
(f)
| < 1 for all
f
such that
∠(
H
PA
(f)H
f
(f))
=
n
360° where
n
is any integer. However, note that the talker might move
the microphone slightly. Furthermore, the talker’s own movements could cause phase
changes in
H
f
(f)
that are difficult to predict. Thus, to be sure that the feedback system is
stable, the phase requirement is no longer particularly helpful. That is, to be sure that the
system is stable, we need the following at all frequencies
f
: |
H
PA
(f)H
f
(f)
| < 1
3
Proper sound design can help alleviate howling. Often the speaker is placed in front of
the microphone, and since both the microphone and speaker are directionally-dependent,
this configuration can significantly reduce |
H
f
(f)
|. Well-versed sound technicians will also
often test the system by increasing the gain until feedback occurs and then apply notch
filters corresponding to the peaks in the loop transfer function. By flattening out the
spectrum, these sound technicians are actually increasing the amount of power that can be
reproduced by the sound system before howling sets in.
However, in some situations, too many notch filters would be required to avoid
significantly changing the signal, and the loop gain of the system will simply need to be
decreased. This solution can be undesirable in many instances, and PA’s that could
automatically adjust themselves to their surroundings would be easier to use.
Furthermore, by taking advantage of the increase in the allowable loop gain, the distance
between the talker and the microphone could be increased, which would help provide an
unobstructed view of the talker.
It is important to note that howling tends to occur at one particular frequency. Before
howling occurs, the loop transfer function has magnitude less than 1 at all frequencies.
Then, as howling begins to set in, the transfer function’s magnitude will exceed 1,
possibly at several different frequencies. Generally, the frequency for which the loop
transfer function has the highest magnitude will grow faster than the others and “win the
race.” This can be considered the dominant eigenfrequency of the loop transfer function.
Various techniques for overcoming acoustic feedback cancellation will be studied in this
report. Most of them rely on using adaptive filters that are trained using the least-mean
squares (LMS) algorithm to cancel the feedback.
4
2.0
Previous Work
2.1
Adaptive Periodic Noise Canceller (APNC)
The earliest work of which we are aware was carried out by J.B. Foley in 1989. It relies
on the fact that howling is periodic, while speech is not when viewed over a long enough
time scale. Foley used an adaptive periodic noise canceller (APNC), as depicted in Figure
3, to eliminate sinusoidal components from the speech signal
1
. The delay
D
was chosen
to be large enough such that the speech was largely uncorrelated with itself, while
D
was
small enough such that the howling could be cancelled before it grew too much in
magnitude. We chose
D
corresponding to 2ms for our experiments although the exact
value was not particularly crucial.
Figure 3. Block diagram of the adaptive periodic noise canceller (APNC)
2.2
Feedback Noise Canceller (FBNC)
The feedback noise canceller (FBNC) is a more common topology used in hearing aids
and is shown in Figure 4. Again a delay
D
is required to reduce the correlations in the
speech
2
. By making
D
correspond to the same delay imposed by the cascade of the ADC
and DAC, the adaptive filter can be made to converge to a transfer function that models
the transfer function of the cascade of the DAC, speaker, room, microphone, and ADC.
This configuration uses the transfer function estimate to subtract out an estimate of the
feedback signal at the microphone. Note that
D
may be chosen much larger than in the
case of the APNC since the ADC and DAC delays can be quite long.
5
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