Rane - Understanding Acoustic Feedback and Suppressors, dokumenty, Akustyka
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UNDERSTANDING ACOUSTIC FEEDBACK & SUPPRESSORS
Understanding Acoustic
Feedback & Suppressors
Introduction
Acoustic Feedback (also referred to as the Larsen ef-
fect) has been roaming around sound reinforcement
systems for a very long time, and everyone seems to
have their own way to tame the feedback lion. Digital
signal processing opened up the microphone to some
creative solutions, each with its own unique compro-
mises. his article takes a closer look into that annoy-
ing phenomenon called acoustic feedback and some of
the DSP based tools available for your toolbox.
• Adaptive Filter Modeling
• Frequency Shifting
• Automatic Notching
Dana Troxel
Rane Corporation
RaneNote 158
© 2005 Rane Corporation
Feedback & Suppressors-
Gaining Insight into Feedback
Every typical sound reinforcement system has two
responses, one when the microphone is isolated from
the loudspeaker (open-loop) and a diferent response
when the microphone is acoustically coupled with the
loudspeaker (closed-loop). he measured response of
the output of a system relative to its input is called its
transfer function
. If the measured open-loop response
of a system has constant magnitude across the frequen-
cy range of interest you can model the system using
a level control followed by some delay. Looking at the
transfer function of a simple level change and delay ele-
ment can provide insight into the behavior of acoustic
feedback in real world situations.
he top half of igure 1 compares two magnitude
responses. he lat (blue) line represents the magni-
tude of an open-loop system (no feedback) with unity
gain (0 dB) and 2 ms of delay. he peaked (red) curve
is the same system after the feedback loop is closed.
he closed-loop has peaks that correspond with zero
degree phase locations shown in the lower half of the
igure. he closed-loop valleys correspond with the 180
degree phase locations. Feedback is a function of both
magnitude and phase. Even though the open-loop gain
is the same at all frequencies, only frequencies that are
reinforced as they traverse the loop (near zero degrees
of phase shift) will runaway as feedback.
Figure 2 shows the efects of reducing the gain by 3
dB and increasing the delay to 10 ms. Notice that the
closed-loop gain reduces signiicantly (more than the 3
dB of open-loop attenuation that was applied) and that
the potential feedback frequencies (areas of 0 degrees
phase shift) get much closer together. he zero degree
phase locations repeat every 360 degrees of phase
change. For a linear phase transfer function you can
calculate the frequency spacing of potential feedback
locations as a function of delay time. he equation for
calculating the delay time is:
Delay Time (sec) = -∆Phase / (∆Frequency x 360)
When ∆Phase = 360 degrees (the phase diference be-
tween two 0 degree phase locations), this leaves:
∆Frequency = 1 / Delay Time (sec)
when ∆Phase is 360 degrees
his means that the potential feedback frequency
spacing = 1 / delay time (in seconds). he following
shows the
potential
feedback frequency spacing for
various delays.
1 / 0.002 sec.
= 500 Hz spacing (for 2 ms of delay)
1 / 0.010 sec.
= 100 Hz spacing (for 10 ms of delay,
shown below)
1 / 0.1 sec.
= 10 Hz spacing (for 100 ms of delay)
his implies that adding delay makes the potential
for feedback worse (i.e. there are more potential feed-
back frequencies because they are closer together).
Practical experience will tell you otherwise. his is
because delay also afects the rate at which feedback
grows and decays. If you have 10 ms of delay between
the microphone and loudspeaker and +0.5 dB of trans-
fer function gain at a potential feedback frequency,
then feedback will grow at a rate of 0.5 dB / 10 ms or
Figure 1. Open (lat) / Closed (peaked) Loop Responses,
Delay = 2ms, Gain = 0 dB
Figure 2. Open (lat) / Closed (peaked) Loop Responses,
Delay = 10 ms, Gain = -3 dB
Feedback & Suppressors-
+50 dB / second. If you increase the delay to 100 ms
then the growth rate slows to +5 dB / second.
Here is another observation regarding gain and its
relationship to feedback: For a ixed delay you can cal-
culate the growth rate of a feedback component if you
know how far above unity gain the open-loop system is
at a particular feedback frequency. his means that if
you are at a venue and can hear feedback growing (and
can estimate its growth rate) you can calculate roughly
how far above unity gain the system is (this also means
your kids probably call you a nerd).
As an example if you estimate that feedback is grow-
ing at a rate of 6 dB / second and you know that the
distance from the loudspeaker to microphone is 15 feet
then you know that the gain is roughly only (6 x 0.015)
or 0.09 dB above unity gain. So… you only need to pull
back the gain by that amount to bring things back into
stability.
Of course the rate of change also applies to feedback
as it decays. If you pull the gain back by 0.09 dB the
feedback will stop growing. If you pull back the gain by
0.2 dB then the feedback frequency will decay at close
to the same rate that it was growing. If you reduce the
gain by 3 dB (below the stability point of unity) it will
decay at a rate of 200 dB / second.
Note also that anything that changes phase will
afect the feedback frequency locations. his includes
temperature changes as well as any iltering and delay
changes. If you analyze how temperature changes af-
fect the speed of sound and look at the corresponding
efective delay change that a temperature shift yields,
you end up with an interesting graph. Figure 3 shows
the shift of a feedback frequency based solely on how
temperature afects the speed of sound. he interesting
points are that feedback frequency shifts are larger at
higher frequencies and the potential for feedback fre-
quency shifts could be signiicant (depending on your
method of control), but more on this later.
To summarize:
• Feedback is both a magnitude and phase issue.
• Increasing system delay, increases the number
and reduces the spacing, of potential feedback
frequencies.
• Delay also afects the rate at which a feedback fre-
quency grows or decays.
• To bring a runaway feedback frequency back into
control you simply need to reduce the gain below
unity. However, it will decay at a rate based on its
attenuation and delay time.
• Temperature changes (and anything else that afects
phase) afect the location of feedback frequencies.
Figure 3. Feedback Frequency Shift vs Frequency
(for six temperature changes)
Feedback & Suppressors-
Methods for Controlling Feedback
Understanding feedback is one thing, taming it is quite
another. here are three main methods used by equip-
ment manufacturers for controlling feedback. he
Adaptive Filter Model method (similar to a method
used in acoustic echo cancellation), the Frequency
Shifting method and the Auto-Notching method. Most
of this discussion is on auto-notching as it is the most
commonly used method.
A sound reinforcement application is shown in
igure 5. Here there is no far-end speech to feed the
model. he local speech is immediately sent out the
loudspeaker and is the only training signal available.
he fact that the training signal is correlated with the
local speech (seen as noise to the training process)
provides a signiicant problem for the adaptive ilter
based modeling. his is particularly true if it is try-
ing to maintain a model that is accurate over a broad
frequency range.
To overcome this problem some form of decorrela-
tion is introduced (such as a frequency shift). his helps
the broad band modeling process but adds distortion
to the signal. As with the teleconferencing application
if the model is not accurate further distortion occurs.
he decorrelation, along with any added distortion due
to an inaccurate model, makes this method less appeal-
ing for some venues. he big advantage to this type of
a feedback suppressor is that your added gain before
feedback margin is usually greater than 10 dB.
Adaptive Filter Modeling
his method is very similar to algorithms used in
acoustic echo cancellation for teleconferencing sys-
tems. he idea is to accurately model the loudspeaker
to microphone transfer function and then use this
model to remove all of the audio sent out the local
loudspeaker from the microphone signal.
Figure 4 shows a teleconferencing application. he
audio sent out the loudspeaker originates from a far-
end location, and the removal of this audio from the lo-
cal near-end microphone keeps the far-end talker from
hearing his own voice returned as an echo. he far-end
talker’s voice is used as a training signal for the mod-
eling. his modeling is an ongoing process since the
model needs to match the ever-changing acoustic path.
During this modeling any local speech (double talk)
acts as noise which can cause the model to diverge. If
the model is no longer accurate then the far end speech
is not adequately removed. In fact, the noise added
from the inaccurate model can be worse than not at-
tempting to remove the echo at all. Much care is taken
to avoid the divergence of the path model during any
periods of double talk.
—
—
Decorrelation
Far End Speech
Near End Speech
Figure 4. Adaptive Filter As Used In Acoustic Echo Cancellation
Figure 5. Adaptive Filter As Used In Feedback Suppression
Feedback & Suppressors-
Frequency Shifting
Frequency shifting has been used in public address
systems to help control feedback since the 1960’s. Feed-
back gets generated at portions of the transfer function
where the gain is greater than 0 dB. he loudspeaker
to microphone transfer function, when measured in a
room, has peaks and valleys in the magnitude response.
In frequency shifting all frequencies of a signal are
shifted up or down by some number of hertz. he basic
idea behind a frequency shifter is that as feedback gets
generated in one area of the response it eventually gets
attenuated by another area. he frequency shifter con-
tinues to move the generated feedback frequency along
the transfer function until it reaches a section that
efectively attenuates the feedback. he efectiveness
of the shifter depends in part on the system transfer
function.
It is worth pointing out that this is not a “musi-
cal transformation” as the ratio between the signal’s
harmonics is not preserved by the frequency shift. A
person’s voice will begin to sound mechanical as the
amount of shift increases. While “audible distortion”
depends on the experience of the listener most agree
that the frequency shift needs to be less than 12 Hz.
How much added gain before feedback can be rea-
sonably expected? he short answer is only a couple
of dB. Hansler
1
reviews some research results that
indicate that actual increase in gain achieved depends
on the reverberation time as well as the size of the
frequency shift. Using frequency shifts in the 6-12
Hz range, a lecture hall with minimal reverberation
beneited by slightly less than 2 dB. An echoic chamber
with reverberation time of greater than 1 second could
beneit by nearly 6 dB by the same frequency shift.
Digital signal processing allows frequency-shifting
techniques in a large variety of applications. When
used in conjunction with other methods such as the
adaptive ilter modeling previously mentioned, it can
provide an even greater beneit. However, the artifacts
due to the frequency shifting are prohibitive in areas
where a pure signal is desired. Musicians are more sen-
sitive to frequency shifts, so think twice before placing
a shifter in their monitor loudspeaker path.
Automatic Notching
Automatic notch ilters have been used to control feed-
back
2
since at least the 1970’s. Digital signal processing
allows more lexibility in terms of frequency detection
as well as frequency discrimination and the method of
deploying notches. Auto-notching is found more fre-
quently among pro-audio users than the other methods
because it is easier to manage the distortion.
When considering automatic notching algorithms
there are three areas of focus: frequency identiication,
feedback discrimination and notch deployment.
Frequency Identiication
Frequency identiication typically is accomplished by
using either a version of the Fourier transform or an
adaptive notch ilter. Both methods of detection al-
low the accurate identiication of potential feedback
frequencies. While the Fourier transform is naturally
geared toward frequency detection, the adaptive notch
ilter can also determine frequency by analyzing the
coeicient values of the adaptive ilter. However, detec-
tion of lower frequencies (less than 100 Hz) are prob-
lematic for both algorithms. Fourier analysis requires
a longer analysis window to accurately determine
lower frequencies and the adaptive notch ilter requires
greater precision.
Feedback Discrimination
here are two main methods used in discriminating
feedback from other sounds. he irst method focuses
on the relative strength of harmonics. he idea is that
while music and speech are rich in harmonics feedback
is not.
Note that either of the frequency detection methods
(Fourier transform or adaptive notch ilter) could be
used to determine the relative strength of harmonics. It
is easier to think in terms of harmonics if you are using
a Fourier transform, but just as frequency can be deter-
mined by analyzing coeicients so also can analyzing
the relationships between sets of coeicients identify
harmonics.
here are drawbacks in utilizing harmonics as a
means of identifying feedback. First, feedback is propa-
gated through transducers and transducers have non-
linearities. his means that feedback (especially when
clipped) will have harmonics. Also, feedback does not
always occur one frequency at a time. If you remember
the discussion on the properties of feedback there is
Feedback & Suppressors-
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