Note: Descriptions are shown in the official language in which they were submitted.
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LOW COST CONTRO~,~,F.R
This invention relates to a low cost active noise cancellation system. It was
s designed by the need for very low cost electronics in using active noise cancellation for
quieting small fans, refrigerators and other extremely cost sensitive applications. The
instant invention has the ability to cancel stationary random noise such as thatencountered on a rangehood fan or tonal noise. The "plant" of the operation, i.e., the
speakers, enclosure, microphone and the configuration itself has to be of a certain
10 design so as to minimi7e delays which interfere with the plants ability to produce a
cancellation signal. These delays are the result of the response of the loudspeaker, its
cabinet and the transit time between speaker and micr~holle. While lcpe~ e
compenc~ting techniques can be used in repetitive noise, they don't work with random
noise. This invention conlc,ll~lates employing strict design criteria in designing the
ls "plant" and using eqn~li7ing filters. The equalization filter allows for a relaxation of
the strict time delay requL,clllenl~. A filter is used to produce an estim~te of the noise
by subtracting the predicted effects of the c~ncell~tion signal from the residual signal.
For tonal cancellation the equalization filter is used to add ~rldition~l delays at
frequencies where nee le-l, for instance where the plant delay is too long to meet the
20 requirements for random cancellation, in order to meet an earlier cycle of the tonal
noise. For random cancellation the equalization filter minimi7es the mean-squareerror resulting from twin delays in the system.
The DVE (digital virtual earth) system disclosed in U.S. Patent No. 5,105,377
can, with a dozen or so taps, cancel band limited random noise if plant delays are small
25 enough. This has been done by canceling random noise limited between lS0Hz to 450
Hz shown in the charts of Figs. 12 and 13 herein. The adaptive FIR filter of DVE can
be replaced by a single inverting amplifier with adjustable gain under a~r~,iate plant
criteria. Thus a small, low cost canceller consists of a single filter to predict the effects
of the cancellation signal on the residual signal en~hling the feedback to be
30 electronically subtracted. An inverting amplifier with adjustable gain is used and,
~Q~53
possibly, an equalization circuit is used to compensate for delays in the plant that al~e too
long for random cancellation when applying the device to tonal cancellation. The DVE
feedback filter can be replaced with a simple delay resulting in a cancellation system
including equalization that requires only a single filter.
According to one aspect of the invention there is provided a low cost active
noise control system for cancelling band-limited random noise in a physical plant,
comprising: a speaker means which, responsive to a control signal, generates a sound
field which operates to cancel said band-limited random noise thereby producing a
residual noise equal to the difference of said sound field and said band-limited random
10 noise; a single error sensing means which senses the residual noise and generates a
residual signal representative of said residual noise; a controller means which comprises
a single inverting amplifier means having an adjustable gain and which, responsive to a
corrected signal, generates said control signal; a compensation means which, responsive
to said control signal, produces a compensation signal; and a subtraction means which
5 subtracts said compensation signal from said residual signal to produce said corrected
signal.
According to another aspect of the invention there is provided a method for
cancelling band limited random noise in a physical plant, comprising the steps of:
generating a control signal by inverting and adjusting the gain of a corrected signal;
20 generating a compensation signal in response to said control signal; subtracting said
compensation signal from a residual signal to produce said corrected signal; generating a
sound field in response too said control signal; wherein said sound field operates to
cancel said band-limited random noise thereby producing a residual noise; sensing the
residual noise using a single sensing means; and generating said residual signal which is
2 5 representative of the residual noise.
Accordingly, it is an object of this invention to provide an active noise
cancellation plant system that can cancel band limited random noise.
Another object of this invention is to provide a low cost active noise cancellation
system.
3 o A further object of this invention is to provide an active noise cancellation
system that can cancel tonal noise.
~ li 4 ~ ~ 5 ~ ~
2a
These and other objects will become apparent when reference is had to the
accompanying description and drawings in which
Fig. I shows a circuit diagram of a basic standard controller set.
Fig. 2 shows a circuit of a basic controller simplified per this invention.
Fig. 3 is a circuit diagram showing a basic/weight optimum filter circuit.
Fig. 4 is a circuit diagram showing a weight optimum filter with an equalizer.
Fig. 5 is illustrative of a circuit showing equalizer training position.
Fig. 6 is a diagram showing an alternate equalizer position.
Fig. 7 shows a canceller with plant equalization.
Fig. 8 shows a diagram of a basic low cost canceller.
Fig. 9 shows a single filter low cost canceller with equalization.
Fig. 10 shows a plot of random noise cancellation in a SAAB twin prop.
Fig. I l shows the plot of random noise cancellation in a Grumman Tiger single
prop.
Figs. 12 and 13 show the results of fan noise cancellation with DVE cancellationOn and Off.
Figs. 14 and 15 show the amount of cancellation without equalization plotted forvarious frequencies and time delays.
~ ..
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Fig. 16 shows the value of Aopt witho~t equalization for vaIious frequencies
and time delays.
Fig. 17 shows the plot of solving for maximum plant delay at various
frequencies, and
s Fig. 18 shows the required phase response for three dir~.~;nt levels of cancellation.
Plant delays prevent an active cAncellAtion system from using perfect
knowledge of the noise to produce the cancellation signal. Plant delays in acoustic
systems often result from the response of the loudspeaker, its cabinet and the transit
time between the speaker and microphone. These delays can be compensated for when
canceling repetitive noise. However, these repetitive cc)lll~e ~A~ g techniques do not
work with random noise.
Insight into the effects of plant delays on random noise cancellation and the
resulting o~LilllUlll plant design can be obtained from an analysis of a simple active
canceller in which the noise is known and is sinusoidal but use is not made of
sinusoidal colllpellsation techniques.
The Active Canceller Model
When the noise is known a simple active canceller can be used consisting of an
inverting amplifier with adjustable gain. If the noise is
n(t) = sin (c3 t), Eq. (l)
where ~ is the frequency in radians per second, then the O~illlUlll cancellation signal is
c(t) = - A ¦ H ¦ sin (c~) t - w td) Eq. (2)
where A is the gain, I H I is the m~gnitude of the plant response at frequency Cl~ and td
is the plant delay, in seconds, at frequency cl~. The residual signal is
r(t) = sin (c~ t) - A IH I sin (~ t - ~ td) Eq. (3)
and the average power of the residual is given by
P=0.5[1-2 A IHI COS(~td)+A2 IHI 2] Eq.(4)
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Plant Desi~n Requirements
Taking the partial derivative of equation 4 with respect to A and solving; the
optimal value of A is
Aopt = Cos(c~td ) Eq. (5)
Note that the optimal gain depends on the frequency, the amount of delay and
the m~gnit~l~le of the frequency response. In order for Aopt to be mdëpendent offrequency the right hand side of equation 5 must be constant. If th'e plant has a flat
frequency response the product ~ td must be constant. This implies that the phase
decreases proportionately to the log of the frequency.
The amount of cancellation is computed by dividing by the power of the
original signal (0.5) giving
dB=lOlog[1-2A ¦H¦cos(c3td) +A2 ¦H¦ 2] Eq.(6)
or
dBopt = 10 log sin2(~ td) Eq. (7)
15 with a flat frequency response
In figures 14 and 15 the amount of cancellation is plotted for various
frequencies and time delays. The plots are, of course, the same with frequency and
delay interchanged since the amount of cancellation depends on the product of the two.
Note that complete cancellation of the sinusoidal noise is obtained whenever the20 product of the frequency, in Hz, and the delay, in seconds, is an integer multiple of 0.5
cycles.
The value of Aopt is shown for various frequencies and time delays in figure
16. Again, the values of frequency and time delay can be interchanged. When either
the frequency or time delay is low, e.g., 100 Hz or 100 I,lsecs, the optimal gain is
25 relatively independent of the other variable. However, when both increase the optimal
gain can swing from +1 to -1.
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A feel for the implications of these results can be obtained by solving for the
maximum plant delay at various frequencies for selected amounts of cancellation.These are listed in table 1 and shown in figure 17 using optimal gain.
s Maximum Delay (llsecs)
Frequency (Hz) 3 dB Cancellation 6 dB Cancellation 12 dB Cancellation
100 1,253 836 404
500 251 167 81
1000 125 84 40
Table 1 . lVI~;...Il..l Delay vs Frequency and l~inimllm Cancellation
A specification for the plant design can be obtained by the use of equations 5
and 7. In order to have constant gain with a flat frequency response the product ct~ td
10 must be constant; call it K.
K=~td Eq. (8)
The value of K can be determine~l by selecting a desired amount of cancellation
and applying equation 7 as follows:
K =sin~' [ log [ 20 ]] Eq. (9)
Table 2 show the values of K and the resulting gains for 3 dB, 6 dB and 12 dB
of cancellation.
Cancellation K A
3 dB 0.787 0.71
6 dB 0.525 0.87
12 dB 0.254 0.97
Table 2. K and A vs Desired Cancellation
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Applying equation 8 gives the required delay at each frequency. Solving the
equation
td = --- Eq. (10)
dcl)
for phase provides the required phase response
~ = -K ln ((d) Eq. (l l)
Figure 18 shows the required phase response for three di~ferent levels of
cancellation. The phase response for the required amount of cancellation and flat
m~gnin~de frequency response provide the specification for the op~illlum plant.
This analysis applies a random c~ncell~tion technique to sinusoidal noise in
order to assess the effects of time delays in the plant. Relationships are derived that
determine the optimal gain and the amount of cancellation for various combinations of
frequency and plant delay. The m~ximl1m plant delay allowable in order to achieve
certain cancellation goals is t~bu1~ted Design rules are presented to determine the
15 optimum plant response.
EQUALIZING FILTER
The low-cost noise cancellation system consists of a microphone, a speaker and
signal processing to minimi7e the noise at the microphone. The speaker is modeled as
20 a discrete transfer function h(z) along with a discrete time delay z~-d of d samples.
The basic system is as follows:
l n
z~d h (z)
-- z~-d (esth(z))
- 1 --
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The canceling signal appears at 1. This signal goes through the time delay and
speaker to be mixed with the noise n. It also goes through an FIR estimate of the
speaker h(z) with the a~plo~uliate time delay. This configuration results in thecanceling signal being subtracted from the noise n before the inversion block. Thus,
the noise n itself is inverted and outputs as the canceling signal.
The problem with this configuration is the canceling signal phase shift caused
by both the time delay d and the speaker h(z). For a low cost canceller it is counter
productive to design in predictors to predict the noise d samples into the future. Rather
it was initially thought to compensate the canceling signal at point 1. The form of this
compensation would be one over the estim~tP of h(z). Nothing can be done about the
delay other than increasing the s~mpling rate to ~ i7e its effects. Here, two filters
along with A/D's and D/A's are needed.
This invention contemplates a configuration that compen~tes for the phase
shifts in the speaker but needs only one filter and associated har.lw~e. The
compensation here consists of the inverse estim~te of the speaker. Here the canceling
signal is sent to the speaker and the time delay feedback function. The signal is
degraded by the speaker and then has noise added to it. This res-llt~nt signal is then
compen~ated This output is added to the negated, delayed only canceling signal. The
result is n only going to the inverter as before.
Many cancellation schemes have been developed such as that in Fig. 1 denoted
as 10 which uses a reference microphone 12, a speaker actuator 14, controller 11 and
an error microphone 13. A substantial amount of signal processing including adaptive
filtering is done in the processor. A simplification to this scheme is seen in Fig. 2 at
20. Here, one error microphone 21 and actuator 22 along with controller 23 having the
necessary signal processing duel adaptive filtering are required. However, even with
p~ a~lling two of the adaptive filters, one multiweight adaptive filter is constantly
having ItS weight values updated which still involves a nontrivial amount of signal
processlng.
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Low Cost Controller Derivation
The new system is a simplified solution of an op~ ulll Weiner filter with a
single gain inversion process that is calculated with a knowledge of the input noise
statistics and the plant characteristics. This system is seen in Figure 3 as 30 with a
feedback filter (an estimate of the delay and plant characteristic) to subtract out the
effect of the canceling signal. It has Gain Determin:~tc r 34, actuator 36, input 3 l,
summing module 32, the gain 33, delay and actuator est1m~te and actuator 35. Thus,
the residual is simply the resultant noise following ca~cellation. Note that the feedback
filter is dependent only on the delay and actuator and needs to be determined only
O once, such as with a white noise training signal.
The fee~bacl~ filter is the impulse response of the actual actuator with delay
included and can be measured t;,~ nt~lly with an analyzer.
The ~lilllulll filter is a realization of the well known projection theorem found
in many stochastics processes texts. Note that this filter is possible only with the
perfect subtraction of the canceling signal. It can be shown that the o~ ulll gain is
such a filter is
gain opt = ~u,n>/<u,u>
Where n is the input noise to be canceled and u is that noise filtered through the
delay and actuator. <> is expectation and the gain equation reduces to
gain opt = cross correlation of n and filtered n at delay divided by the auto
correlation of filtered n
Therefore, the primary disadvantage to the low cost scheme is readily apparent
- the transport delay can cause the O~Lilllulll gain to be so low as to effect no
cancellation of n. However, given a reasonable delay, say 2 sample periods,
c~ncell~tion can be effected if the cross correlation at 2 is not too small. So, white
noise cannot be canceled with this scheme but correlated signals, especially those
whose frequency is much less than the digital sampling freguency can be significantly
reduced.
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E~ualization of Plant
An improvement to the new system is realized with an equalizer placed after
the gain block as in Figure 4 as 40 having modules input 41, summer 42, gain 43,equalizer 46, delay and actn~tor estimator 44 and actuator 45.
The equalizer 46 is determined analytically or adaptively (such as with a white
noise training signal). A conventional equalizer would be trained so that the
convolution of the equalizer and actuator is an impulse. However, for this control
system application, the resulting delay is unacceptable. So, given an impulse response
of interest, the equalizer is trained to produce the correct phase shift at frequencies of
o interest. As with a feedbaçk filter, the equalizer is dependent only on the actuator and
need be det.ormined only once for a given plant. Thus the signal processing is reduced
to two filters only with no filter weight adaption processing necessary during
operation.
This unique equalizer is trained as in Fig. 5. The input is the set of frequencies
to be corrected. The frequency response of the plant will give the phase shift and
m~nitude response through the plant. Then determine the frequencies to be equalized
(from a knowledge of the noise to be canceled) and construct the input to the training
process. A~-lition~l emphasis may be given to the specific frequencies of interest by
increasing their relative m~gnitude going into the equalizer. Note also that frequencies
that should not be canceled such as voice or alarms may have their phases shifted so as
to add constructively at the microphone and ensure their being heard.
This scheme in Fig. 4 works well but requires two sets of A/D's and D/A's to
support the two digital filters. An alternative scheme was devised to further reduce the
hardware requi~ ents in this low cost c~nceling approach.
WO94/01810 2~ 4~S3 PCI/US92/05772
Sin~le Filter Equalization
A further improvement in the way of hardware reduction is seen in Fig. 6 as 60
with modules input 61, summPr 63, equalizer 62, gain 64, delay only 65 and actuator
66.
Here, the equalizer 62 is placed after the microphone and before the subtractionof the canceling signal. The feedback filter is reduced to a delay only; the equalizer 62
produces the corrected version of the canceling signal still incorporating the delay at
the feedback cancellation point. Therefore, only one digital filter with a simple delay
feedback filter is needed in this low-cost implementation.
0 Training the equalizer is identical to the two filter canceller above and the
equalizing filter produced is identical. Note that the residual before the gain inverter is
now not the noise itself but an equalized version of the noise. The residual still has the
canceling signal subtracted from it though. The fee~lback delay can be adjusted to give
the best cancellation when the plant delay is uncertain. Obtaining the impulse response
with the analyzer in the lab usually give a good indication of the delay - the time of the
first peak co~ Jollds to the delay.
The two filter configuration is much less sensitive to the equalizer than the
single filter equalizer due to a good noise sample always being present just before the
inversion process. In the one filter case, an equalized version of the noise was present
at the inverter. This example was with plant of l00 weights and an equalizer of 32 and
then l00 weights. A different plant with a more over damped step response, shorter
transport delay, longer equalizer or noise with different statistics may make the one
filter case practical.
A sample low cost canceller with plant equalizations shown in Fig. 7 as 70 with
2s microphone 77, amplifier 7 l, summer 72, filter 73, equalizer 74 and adjustable gain
amplifier 75.
Fig. 8 shows basic low cost canceller 80 with microphone 86, amplifier 81,
summ~tion 82, filter 84 and amplifier 83. The use of a single filter low cost canceller
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with eqll~li7~tion is shown as 90 with equalization feedback cancellation 91, summer
92, delay 93, amplifier 94, actuator 95 and microphone 96.
Fig. 10 shows the plot for a prop plane noise where the gain was adjusted for
optimum performance once the fee~lb~ck filter was loaded. The peak reduction was 10
5 dB for the lowest harmonic and a~pro~ ately S dB for the next lowest.
Fig. 11 shows the plot for a single engine having a broader spectrum without
high peaks at low frequency. The reduction was 3 - 5 dB across the spectrum.
