Rane - Understanding Acoustic Feedback & Suppressors, dokumenty, Akustyka
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UNDERSTANDING ACOUSTIC FEEDBACK & SUPPRESSORS
Understanding Acoustic
Feedback & Suppressors
Introduction
Acoustic Feedback (also referred to as the Larsen efect)
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
compromises. 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 frequency 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 element 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 magnitude 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 attenua-
tion that was applied) and that the potential feedback frequen-
cies (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 func-
tion of delay time. he equation for calculating the delay time is:
When ∆Phase = 360 degrees (the phase diference between
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 feed-
back worse (i.e. there are more potential feedback 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 loudspeak-
er and +0.5 dB of transfer function gain at a potential feedback
frequency, then feedback will grow at a rate of 0.5 dB / 10 ms
or +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 relation-
ship to feedback: For a ixed delay you can calculate 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).
Delay Time (sec) = -∆Phase / (∆Frequency x 360)
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-
As an example if you estimate that feedback is growing 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 de-
cays. 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 grow-
ing. 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 afect 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 af-
fects the speed of sound. he interesting points are that feedback
frequency shifts are larger at higher frequencies and the potential
for feedback frequency shifts could be signiicant (depending on
your method of control), but more on this later.
Methods for Controlling Feedback
Understanding feedback is one thing, taming it is quite an-
other. here are three main methods used by equipment manu-
facturers 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 com-
monly used method.
Adaptive Filter Modeling
his method is very similar to algorithms used in acoustic
echo cancellation for teleconferencing systems. he idea is to ac-
curately 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 local 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
modeling. 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 attempting to remove the echo at all. Much
care is taken to avoid the divergence of the path model during
any periods of double talk.
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) pro-
vides a signiicant problem for the adaptive ilter based model-
ing. his is particularly true if it is trying to maintain a model
that is accurate over a broad frequency range.
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 frequency
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) af-
fect the location of feedback frequencies.
—
Far End Speech
Near End Speech
Figure 3. Feedback Frequency Shift vs Frequency
(for six temperature changes)
Figure 4. Adaptive Filter As Used In Acoustic Echo Cancellation
Feedback & Suppressors-
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 tech-
niques in a large variety of applications. When used in conjunc-
tion 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 prohibi-
tive in areas where a pure signal is desired. Musicians are more
sensitive 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 feedback
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 frequently 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 discrimi-
nation and notch deployment.
Decorrelation
Figure 5. Adaptive Filter As Used In Feedback Suppression
To overcome this problem some form of decorrelation 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
appealing 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.
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 allow the accurate identii-
cation 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, detection
of lower frequencies (less than 100 Hz) are problematic for both
algorithms. Fourier analysis requires a longer analysis window to
accurately determine lower frequencies and the adaptive notch
ilter requires greater precision.
Frequency Shifting
Frequency shifting has been used in public address systems
to help control feedback since the 1960’s. Feedback gets gener-
ated 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 magni-
tude 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 continues 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 “musical trans-
formation” 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 the 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 reasonably ex-
pected? 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
Feedback Discrimination
here are two main methods used in discriminating feed-
back 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 fre-
quency can be determined 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 propagated 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 potential for a feedback frequency anywhere the phase of the
loudspeaker to microphone transfer function is zero degrees. For
a system with 25 ms of delay (roughly 25 ft) this occurs every 40
Hz, and the zero degree frequency locations get closer together
Feedback & Suppressors-
as the delay increases. It is not possible to ensure that simulta-
neous feedback frequencies will never be harmonically related.
he potential for feedback with harmonics needs to be balanced
against the fact that some non-feedback sounds (tonal instru-
ments such as a lute) have weak harmonics, blurring the area of
accurate discrimination.
Another method for discriminating feedback from desirable
sound is to analyze feedback through some of its more unique
characteristics. his can be done without analyzing harmonic
content. For example a temporary notch can be placed on a
potential feedback frequency. Feedback is the only signal that
will always decay (up stream of the ilter) coincident with the
placing of the notch. However, because placing a temporary
notch is intrusive some other mechanism needs to be used to
identify potential feedback frequencies before a temporary notch
is placed for veriication. One such useful characteristic is that
a feedback frequency is relatively constant over the time that its
amplitude is growing. his constant frequency combined with
a growing magnitude proves very useful as a precursor to the
temporary notch.
efective at controlling feedback during environmental changes
(such as temperature mentioned above) than are low Q (wide),
shallow notches. his means if you use low Q, shallow notches
you will be less likely to have notches deployed that are not
performing any function other then hacking up the hard work
you put in on your frequency response. Most auto-notching
algorithms allow you to select the default width and maximum
depth of the notches used.
How much additional gain before feedback can be achieved
from auto-notching? If you had a perfectly lat frequency
response then the auto-notching algorithm would not provide
any additional gain margin. he best the algorithm can do is
pull down the gain in a inite number of locations. If you had a
handful of peaks then the auto-notch could provide additional
margin based on how much higher the peaks are above the
remaining response. Typically the auto-notch provides only a
couple of dB of additional gain before feedback.
Despite the lack of large additional gain margin there are
still two other signiicant reasons for having an auto-notch in the
system. First, the auto-notch provides a simple tool to aid in the
identiication of problem spots in the response when the audio
system is irst installed. Second, it provides a safety net that can
remain in place to cope with the ever-changing acoustic path
(unwanted additional relections, gain change etc.).
Notch Deployment
he inal area in auto-notching algorithms is the deploy-
ment of the notches. Most auto-notching feedback suppressors
allow the user to identify ilters as either ixed (static) or loating
(dynamic) in nature. his designation refers to the algorithm’s
ability to recycle the ilter if needed. If a feedback frequency is
identiied the algorithm looks to see if a notch has already been
deployed at that frequency. If found the notch will be appro-
priately deepened. If not found then a new ilter is deployed
(ixed ilters are allocated before loating ilters). If all ilters are
allocated then the oldest loating ilter is reset and re-deployed at
the new frequency.
Another useful feature is to give the user the option of having
the algorithm turn down the broadband gain (with a program-
mable ramp back time) instead of recycling a loating ilter if
all ilters are used up. Adjusting the broad band gain does not
increase the gain margin but it does provide a measure of safety
once all of the available ilters are gone.
An area in notch deployment that requires careful atten-
tion is the depth and width of notches used to control feedback
frequencies. To bring a feedback frequency back into stability
the system’s open-loop transfer function gain simply needs to be
below unity at that frequency. A desirable transfer function will
have peaks that are reasonably lat through the frequencies of
interest. he depth of the notch used to control a feedback fre-
quency should not be greater than the relatively hot area of gain
that caused it, plus a little safety margin. his means notches on
the order of a couple of dB, not tens of dB. If the auto-notch-
ing algorithm is placing notches with a depth of 20 dB or more,
something is wrong. One area to look at is the bandwidth of the
notches used.
here is a tendency with these algorithms to try and use
notches that are as narrow as possible, with the mistaken belief
that the cumulative response will be less noticeable. What usu-
ally ends up happening is that several narrow notches get placed
at a depth of 20 dB or more to lower the overall gain 2 or 3 dB
in a larger area. Furthermore, high Q (narrow) notches are less
Conclusions
Acoustic feedback is both a magnitude and phase issue.
As such, changes in the system’s phase response due to delay,
iltering or temperature changes impact potential feedback
frequencies. If notch ilters are used to control feedback they
should be placed after all other changes are made to the system’s
phase response to ensure their utility. hey should also be wide
enough to ensure their ongoing usefulness despite changes to the
feedback path.
In order to bring a runaway frequency back into stability the
magnitude simply needs to be taken below the unity gain mark
plus a couple of dB for a safety margin. In addition to a slightly
expanded gain margin, the auto-notch tool provides a simple
means for ringing out a room as well as leaving a safety net after
the original installation is complete.
In addition to auto-notching algorithms, adaptive ilter mod-
els and frequency shifting algorithms also provide useful ways to
suppress feedback and increase a system’s gain before feedback
margin. An adaptive ilter model based feedback suppressor relies
on an accurate model of the loudspeaker to microphone acoustic
path in order to remove feedback from a receiving microphone.
If the model is inaccurate then distortion can occur. A decorrela-
tion process is used to improve the convergence characteristics
of the broad band adaptive ilter. his decorrelation can also
add a limited amount of distortion. However, the adaptive ilter
model is capable of greater than 10 dB of additional gain before
feedback.
he utility of the frequency shifter depends on the system
where it is applied. As a general rule the frequency shifter will
provide a greater gain margin in a more reverberant space than
in a smaller less reverberant space. he frequency shift should be
kept to less than 12 Hz to minimize audible distortion.
Feedback & Suppressors-
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