B
Bret Cahill
Guest
Is this situation/solution common? There is at least one example in
electronics.
Bret Cahill
electronics.
Bret Cahill
P
Phil Hobbs
Guest
On 09/09/2011 02:50 PM, Bret Cahill wrote:
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
http://electrooptical.net
Autocorrelation and Kalman filtering are a couple of examples.
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
160 North State Road #203
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
http://electrooptical.net
F
Fred Marshall
Guest
On 9/9/2011 11:50 AM, Bret Cahill wrote:
Are you suggesting that there are 2 signals of interest that will each
be filtered using different adaptive filters? That would be one
interpretation in which case asking about 1 signal will do fine.
Or are you suggesting that there are 2 signals and you want to filter
one of them and might use the other as a reference?
Both solutions are common.
The first might be an adaptive line enhancer or ALE in which there is 1
signal in and 1 filtered signal out.
There is no "reference" really, just a delayed version of the input so
that there's no correlation of the noise from the direct input and the
delayed input. Then one or the other is adaptively filtered to minimize
the difference between the direct input and the delayed/filterd version
of it.
The output of the adaptive filter (ahead of the differencer) is the output.
This tends to create a comblike set of bandpasses in the adaptive filter
that passes the periodic parts of the input.
The second might be an adaptive noise canceller (ANC) where there are
two inputs:
- one is the "signal of interest that's perturbed by sinusoidal noise
.... "interference".
- the other is the best capture of the perturbing sinusoidal noise (the
interference) that's possible to get. This is called the "reference".
Then, the reference is filtered so that the difference between that and
the signal of interest is minimized. If it's minimized then the best
possible job of removing the interference.
Fred
I don't know what you mean by "2 noisy signals to be filtered".
Are you suggesting that there are 2 signals of interest that will each
be filtered using different adaptive filters? That would be one
interpretation in which case asking about 1 signal will do fine.
Or are you suggesting that there are 2 signals and you want to filter
one of them and might use the other as a reference?
Both solutions are common.
The first might be an adaptive line enhancer or ALE in which there is 1
signal in and 1 filtered signal out.
There is no "reference" really, just a delayed version of the input so
that there's no correlation of the noise from the direct input and the
delayed input. Then one or the other is adaptively filtered to minimize
the difference between the direct input and the delayed/filterd version
of it.
The output of the adaptive filter (ahead of the differencer) is the output.
This tends to create a comblike set of bandpasses in the adaptive filter
that passes the periodic parts of the input.
The second might be an adaptive noise canceller (ANC) where there are
two inputs:
- one is the "signal of interest that's perturbed by sinusoidal noise
.... "interference".
- the other is the best capture of the perturbing sinusoidal noise (the
interference) that's possible to get. This is called the "reference".
Then, the reference is filtered so that the difference between that and
the signal of interest is minimized. If it's minimized then the best
possible job of removing the interference.
Fred
B
Bret Cahill
Guest
Same reference and same filter for both signals.
The noise in one correlates by negative 1 to the noise in the other so
the sum of one plus some factor times the second signal yields the
reference.
In one situation one signal is pretty clean and the other noisy so the
noisy signal can be filtered with the clean signal alone.
For uniformity or balance the clean signal should be filtered with
itself.
I'll check it out.
Bret Cahill
H
HardySpicer
Guest
On Sep 10, 10:22 am, Bret Cahill <BretCah...@peoplepc.com> wrote:
filter. For speech this usually means a voice-activity detector.
Failing that you might try Independent Component Analysis if you know
the PDF of the signals.
Hardy
You need a "noise-alone" signal for it to work in an ordinary adaptive
filter. For speech this usually means a voice-activity detector.
Failing that you might try Independent Component Analysis if you know
the PDF of the signals.
Hardy
B
Bret Cahill
Guest
Something similar:
http://www.ee.psu.edu/reu/All_journal/2004v2/REUV2_p52p59.pdf
Seems to be able to work on any kind of noise, not just sinusoidal,
with some kind of correlation of the noise in both signals.
If you knew the signal correlation was +1 and the noise correlation
was -1, however, you should be able to exploit the 2nd fact for the
best filter. Just add one signal to a known factor times the other
signal. That reference could then be used to match filter or
otherwise process both signals.
Bret Cahill
B
Bret Cahill
Guest
I forgot to add that both clean signals correlate by +1.
B
Bret Cahill
Guest
This filtering situation is possible in at least one [probably
academic] electronics situation.
Determining the inductance of an inductor with a fluctuating voltage
by dividing that voltage by the 1st derivative of current.
The unknown inductor is wired to an inductor with a known inductance
and the voltage is measured between the two inductors.
An unknown randomly fluctuating voltage source, in the circuit between
ground and the unknown inductor, is the noise that appears in both
signals.
The noise in the signal voltage goes up when the noise in the
derivative of the signal current goes down so the noise in one signal
correlates by -1 to the noise in the other signal.
The noise in the quotient, of course, is worse than the noise in
either signal.
But if you add the noisy voltage to some constant times the derivative
of the current then you get a clean reference for both signals.
Bret Cahill
B
Bret Cahill
Guest
It would be pretty nifty to get a reference named after me.
On the other hand references may be like tornadoes and not get names.
Bret Cahill
F
Fred Marshall
Guest
On 9/9/2011 4:13 PM, Bret Cahill wrote:
sinusoidal" unless you make some rash assumptions that don't hold well
in a number of practical situations. I'm not saying that it *never*
happens but:
A reasonable model is that the "noise" is made up of broadband
components and spectral "lines" or sinusoids. It's easy for the
sinusoidal components to correlate. It's not so easy for the broadband
parts to correlate unless there is very low time delay between the
reference and the signal to be cleaned up.
Noise cancelling headphones work because there is very low time delay
between the "noise" and the headphone active output. In that way,
broadband noise can be subtracted because it's, if you will, highly
correlated. And such implementations aren't even "adaptive" as such.
But, in many other practical situations where adaptation is warranted,
there is quite a delay between the reference and the signal. In this
case there is no hope of reducing broadband noise because uncorrelated
broadband noise cannot subtract from other broadband noise - it only adds.
So, in the paper you reference, I think what they mean by "correlated"
noise is that there are sinusoidal parts - although I don't see that
they mention that - and the rest is likely broadband AND uncorrelated.
Interesting that the paper you cite has as first reference the paper by
Widrow et al. I worked with McCool, Hearn and Zeidler when their paper
was published and got some first hand insights at the time.
Fred
Well, I don't think that "it works on any kind of noise, not just
sinusoidal" unless you make some rash assumptions that don't hold well
in a number of practical situations. I'm not saying that it *never*
happens but:
A reasonable model is that the "noise" is made up of broadband
components and spectral "lines" or sinusoids. It's easy for the
sinusoidal components to correlate. It's not so easy for the broadband
parts to correlate unless there is very low time delay between the
reference and the signal to be cleaned up.
Noise cancelling headphones work because there is very low time delay
between the "noise" and the headphone active output. In that way,
broadband noise can be subtracted because it's, if you will, highly
correlated. And such implementations aren't even "adaptive" as such.
But, in many other practical situations where adaptation is warranted,
there is quite a delay between the reference and the signal. In this
case there is no hope of reducing broadband noise because uncorrelated
broadband noise cannot subtract from other broadband noise - it only adds.
So, in the paper you reference, I think what they mean by "correlated"
noise is that there are sinusoidal parts - although I don't see that
they mention that - and the rest is likely broadband AND uncorrelated.
Interesting that the paper you cite has as first reference the paper by
Widrow et al. I worked with McCool, Hearn and Zeidler when their paper
was published and got some first hand insights at the time.
Fred
M
maury
Guest
On Sep 14, 1:58 am, Fred Marshall <fmarshallxremove_th...@acm.org>
wrote:
physical limitations, not limitations of the algorithm (IIRC ANC uses
Filtered-X not the configuration of the paper). I have put delays in
the reference path to ensure correlation (causality) many times using
broadband noise.
Maurice
wrote:
But Fred, your example is for active noise cancellation (ANC) and its
physical limitations, not limitations of the algorithm (IIRC ANC uses
Filtered-X not the configuration of the paper). I have put delays in
the reference path to ensure correlation (causality) many times using
broadband noise.
Maurice
F
Fred Marshall
Guest
On 9/14/2011 9:21 AM, maury wrote:
I can't imagine that we disagree.
The original question is about active noise cancellation. I don't know
of any other kind of *adaptive* noise cancellation or perhaps I have
some terms off?
I don't get what you mean by "physical limitations" and not "limitations
of the algorithm". As far as I'm concerned, "the algorithm" is all
about how one adapts the filter and not much about how the overall
system works. I wasn't addressing the algorithm at all.
The simple block diagrams in my head pretty much agree with the student
paper that was referenced. In Figure 1, they show an ANC.
(I don't know what your "X" is in "filtered-X")
The point of that diagram is that there is:
S + No ... a signal of interest plus some noise
and
N1 ... a version of No that would ideally be high "SNR" for the
noise and not perturbed (have components of) S.
In this case the stuff that I'm familiar with did not have the luxury of
having the broadband parts of No be correlated with the broadband parts
of N1. So the adaptive filter "shuts off" in frequency bands where
that's all there is. So, it effectively becomes a set of bandpasses for
the sinusoidal components in N1 whose amplitudes and phase are adjusted
by the adapted filter to do the best possible job of cancelling their
presence in No.
But, if there were good correlation between the broadband parts of No
and N1 then a simple delay and scaling might be just the thing - just
like in the noise cancelling headphone case. In that case I'm sure that
there *is* an "adaptation" of sorts:
- first you start out with an inversion
- then you scale to match the headphone characteristics.
OK - it's one-time and manual but that works.
And, of course, just as needed for the Figure 1 diagram to work well,
the signal components in N1 are either zero or very low.
Did I miss something?
Fred
Maury,
I can't imagine that we disagree.
The original question is about active noise cancellation. I don't know
of any other kind of *adaptive* noise cancellation or perhaps I have
some terms off?
I don't get what you mean by "physical limitations" and not "limitations
of the algorithm". As far as I'm concerned, "the algorithm" is all
about how one adapts the filter and not much about how the overall
system works. I wasn't addressing the algorithm at all.
The simple block diagrams in my head pretty much agree with the student
paper that was referenced. In Figure 1, they show an ANC.
(I don't know what your "X" is in "filtered-X")
The point of that diagram is that there is:
S + No ... a signal of interest plus some noise
and
N1 ... a version of No that would ideally be high "SNR" for the
noise and not perturbed (have components of) S.
In this case the stuff that I'm familiar with did not have the luxury of
having the broadband parts of No be correlated with the broadband parts
of N1. So the adaptive filter "shuts off" in frequency bands where
that's all there is. So, it effectively becomes a set of bandpasses for
the sinusoidal components in N1 whose amplitudes and phase are adjusted
by the adapted filter to do the best possible job of cancelling their
presence in No.
But, if there were good correlation between the broadband parts of No
and N1 then a simple delay and scaling might be just the thing - just
like in the noise cancelling headphone case. In that case I'm sure that
there *is* an "adaptation" of sorts:
- first you start out with an inversion
- then you scale to match the headphone characteristics.
OK - it's one-time and manual but that works.
And, of course, just as needed for the Figure 1 diagram to work well,
the signal components in N1 are either zero or very low.
Did I miss something?
Fred
B
Bret Cahill
Guest
The confusion here is probably due some less than clear terminology,
i.e., using one word for two different things.
In the OP it is suggested that a clean reference for use in, say,
match filtering, can be made in some situations by adding one noisy
signal to another noisy signal times some factor.
We know the clean signals correlate by +1 and the noise in the signals
by -1. It's easy to create a nice clean reference from such signals
on SPICE by adding the voltage to the first derivative of current
times an inductance.
Any "noise cancellation" -- if that's what you want to call it -- is
only in cobbling together the reference.
The noisy signals are then sent with that reference to an adaptive
filter to reduce the noise but I wouldn't call that step of the
process "noise cancellation."
Cancellation of noise in a reference is not really the same thing as
cancelling the noise in the signals, although it leads to the same
overall goal
Bret Cahill
The mind invents new things more easily than new words to describe
those things. That's why so many misleading terms appear in language.
-- Tocqueville (pointing out that the U. S. constitution isn't for a
federal, but an "incomplete national government.")
M
maury
Guest
On Sep 14, 3:56 pm, Fred Marshall <fmarshallxremove_th...@acm.org>
wrote:
It's probably all trems. ACTIVE noise cancellation refers the the
generation of a physical anti-noise (using speakers, transducers,
etc.) to effectively cancel out the unwanted noise.This is what is
used in headsets, also around machinary, and so forth. ADAPTIVE noise
cancellation is the reduction of noise on a signal. With active noise
cancellation there can't be much delay because the anti-noise must be
generated *soon enough* to be an effective cancellation signal
What I was refering to was your statement
*But, in many other practical situations where adaptation is
warranted,
there is quite a delay between the reference and the signal. In this
case there is no hope of reducing broadband noise because
uncorrelated
broadband noise cannot subtract from other broadband noise - it only
adds.*
With adaptive noise cancellation (which is waht thw Widrow paper is
addressing) broadband noise can be cancelled, even if the delay is
long, by putting in a delay register to force the signals to be within
the adaptation filter range.
So when you said *adaptation* and referred to the Widrow paper,
ADAPTIVE noise cancellation is what came to mind.
Maurice
wrote:
Fred,
It's probably all trems. ACTIVE noise cancellation refers the the
generation of a physical anti-noise (using speakers, transducers,
etc.) to effectively cancel out the unwanted noise.This is what is
used in headsets, also around machinary, and so forth. ADAPTIVE noise
cancellation is the reduction of noise on a signal. With active noise
cancellation there can't be much delay because the anti-noise must be
generated *soon enough* to be an effective cancellation signal
What I was refering to was your statement
*But, in many other practical situations where adaptation is
warranted,
there is quite a delay between the reference and the signal. In this
case there is no hope of reducing broadband noise because
uncorrelated
broadband noise cannot subtract from other broadband noise - it only
adds.*
With adaptive noise cancellation (which is waht thw Widrow paper is
addressing) broadband noise can be cancelled, even if the delay is
long, by putting in a delay register to force the signals to be within
the adaptation filter range.
So when you said *adaptation* and referred to the Widrow paper,
ADAPTIVE noise cancellation is what came to mind.
Maurice
F
Fred Marshall
Guest
On 9/14/2011 3:32 PM, maury wrote:
In my experience, in adaptive noise cancellation with a reference, there
is NO correlation between the broadband noises. So you can delay all
you want and on either channel and no improvement.
And, you will notice that there is no "delay register" in the ANC block
diagram.
So there must be something about the noise in your reference and the
noise in your signal that allows that delay to have a positive impact.
What is it? I'm curious.
Fred
Well OK but that requires some pretty big constraints on the signals.
In my experience, in adaptive noise cancellation with a reference, there
is NO correlation between the broadband noises. So you can delay all
you want and on either channel and no improvement.
And, you will notice that there is no "delay register" in the ANC block
diagram.
So there must be something about the noise in your reference and the
noise in your signal that allows that delay to have a positive impact.
What is it? I'm curious.
Fred
M
maury
Guest
On Sep 15, 12:20 am, Fred Marshall <fmarshallxremove_th...@acm.org>
wrote:
available. I can use the noise sample as the reference, the noisy
signal as the input, and cancel the noise. I just need to make sure
the noise reference doesn't get to the summer before the output of the
adaptive filter. Thus the delay register in the reference. The delay
can be as long as what is needed to ensure causality.
I have used this to actually reduce correlated signals to measure the
broadband noise (see patents 7603258, 6725705 for details). In this
case, the noise was the seismic rumbling from trucks, cars,clicking
from womens' high-heeled shoes, etc., and the broadband seismic noise
from underground sources was the desired. The adaptive filter produced
an estimate of the noise. Instead of using the error signal (which is
normally the case) , use the adaptive filter output.
There is no constraint on Widrow's LMS filter for the signals to be
correlated signals. The constraint is that the signal and the noise
can't be correlated. The trick is to determine what is the input, what
is the reference, and how do I get the reference.
Maurice
wrote:
Let's say I have a noisy signal, but I have a bit of the noise
available. I can use the noise sample as the reference, the noisy
signal as the input, and cancel the noise. I just need to make sure
the noise reference doesn't get to the summer before the output of the
adaptive filter. Thus the delay register in the reference. The delay
can be as long as what is needed to ensure causality.
I have used this to actually reduce correlated signals to measure the
broadband noise (see patents 7603258, 6725705 for details). In this
case, the noise was the seismic rumbling from trucks, cars,clicking
from womens' high-heeled shoes, etc., and the broadband seismic noise
from underground sources was the desired. The adaptive filter produced
an estimate of the noise. Instead of using the error signal (which is
normally the case) , use the adaptive filter output.
There is no constraint on Widrow's LMS filter for the signals to be
correlated signals. The constraint is that the signal and the noise
can't be correlated. The trick is to determine what is the input, what
is the reference, and how do I get the reference.
Maurice
B
Bret Cahill
Guest
How does the adaptive filter give an estimate of the noise? Does it
require a "noise" reference?
Then it would be wasting information when processing signals that are
correlated.
In the case where the correlation of the signals is +1 and the noise
is -1, the reference depends on what is known.
Bret Cahill
M
maury
Guest
On Sep 15, 12:01 pm, Bret Cahill <Bret_E_Cah...@yahoo.com> wrote:
What started this particular part of your thread (sorry, your thread
got a bit hijacked
) is the idea that you can't have long delays
with broadband noise in an adaptive filter. In the last example I
gave, the desired signal is not the correlated stuff, but the noise.
We weren't exactly addressing the particular configuration you started
with, but it leads back to it.
If I have a boadband noise signal currupted with correlated signals,
when I remove the correlated signals, I have the wanted noise
remaining. In the case of *adaptive noise cancellation* (what Widrow
calls adaptive interference cancellation) the signal is actually the
reference, and the noise is the input to the adaptive filter. This is
the model you showed in the paper. A good analysis of this is in
Widrow's book adaptive signal processing, chapter 11 or 12 IIRC (I
think it's also in the paper he wrote with McCool, et. al.). Widrow
calls this adaptive interference cancellation, rather than adaptive
noise cancellation.
With respect to long delays, with the model you referenced, if the
signal source, S + No gets to the filter before the noise source, N1,
then the filter will not adapt (non-causal). The remedy is to place
delays in the signal line to force causality. It doesn't matter if the
delay is long.
In the paper you referenced, I believe the S + No label should
be after the summation in the signal line. The signal is corrupted
with noise from N1, but the noise N1 gets convolved with some
unknown impulse response to become No. The goal is to estimate this
unknown impulse response so that the sample of noise available, N1,
can be used to reduce the noise level on S. This is precisely the
problem I had. I had a seismic sensor corrupted with noise. The noise
was the seismic rumbling of trucks, cars, etc. The problem was that
the rumbling was convolved with the soil impulse response before it
got to the sensor. This is exactly the model in your reference paper,
only S was broadband seismic noise, and N1 was correlated noise.
To further complicate things, the seismic sensors needed to be placed
a distance from the noise reference, which meant the noise was on the
input of the adaptive filter before the reference. I needed to place a
large delay in line with the reference to make the system appear
causal. Most people are used to seeing the sample noise as the
reference, rather than the input to the adaptive filter.
Hope I'm clearing this up rather than making it more obscure.
Maurice
Bret,
What started this particular part of your thread (sorry, your thread
got a bit hijacked
) is the idea that you can't have long delayswith broadband noise in an adaptive filter. In the last example I
gave, the desired signal is not the correlated stuff, but the noise.
We weren't exactly addressing the particular configuration you started
with, but it leads back to it.
If I have a boadband noise signal currupted with correlated signals,
when I remove the correlated signals, I have the wanted noise
remaining. In the case of *adaptive noise cancellation* (what Widrow
calls adaptive interference cancellation) the signal is actually the
reference, and the noise is the input to the adaptive filter. This is
the model you showed in the paper. A good analysis of this is in
Widrow's book adaptive signal processing, chapter 11 or 12 IIRC (I
think it's also in the paper he wrote with McCool, et. al.). Widrow
calls this adaptive interference cancellation, rather than adaptive
noise cancellation.
With respect to long delays, with the model you referenced, if the
signal source, S + No gets to the filter before the noise source, N1,
then the filter will not adapt (non-causal). The remedy is to place
delays in the signal line to force causality. It doesn't matter if the
delay is long.
In the paper you referenced, I believe the S
+ No label shouldbe after the summation in the signal line. The signal is corrupted
with noise from N1
, but the noise N1 gets convolved with someunknown impulse response to become No
. The goal is to estimate thisunknown impulse response so that the sample of noise available, N1
,can be used to reduce the noise level on S
. This is precisely theproblem I had. I had a seismic sensor corrupted with noise. The noise
was the seismic rumbling of trucks, cars, etc. The problem was that
the rumbling was convolved with the soil impulse response before it
got to the sensor. This is exactly the model in your reference paper,
only S
was broadband seismic noise, and N1 was correlated noise.To further complicate things, the seismic sensors needed to be placed
a distance from the noise reference, which meant the noise was on the
input of the adaptive filter before the reference. I needed to place a
large delay in line with the reference to make the system appear
causal. Most people are used to seeing the sample noise as the
reference, rather than the input to the adaptive filter.
Hope I'm clearing this up rather than making it more obscure.
Maurice
B
Bret Cahill
Guest
So the noise reference still had _some_ signal in it, it just had aWith adaptive noise cancellation (which is waht thw Widrow paper is
addressing) broadband noise can be cancelled, even if the delay is
long, by putting in a delay register to force the signals to be within
the adaptation filter range.
Well OK but that requires some pretty big constraints on the signals.
In my experience, in adaptive noise cancellation with a reference, there
is NO correlation between the broadband noises. So you can delay all
you want and on either channel and no improvement.
And, you will notice that there is no "delay register" in the ANC block
diagram.
So there must be something about the noise in your reference and the
noise in your signal that allows that delay to have a positive impact.
What is it? I'm curious.
Fred
Let's say I have a noisy signal, but I have a bit of the noise
available. I can use the noise sample as the reference, the noisy
signal as the input, and cancel the noise. I just need to make sure
the noise reference doesn't get to the summer before the output of the
adaptive filter. Thus the delay register in the reference. The delay
can be as long as what is needed to ensure causality.
I have used this to actually reduce correlated signals to measure the
broadband noise (see patents 7603258, 6725705 for details). In this
case, the noise was the seismic rumbling from trucks, cars,clicking
from womens' high-heeled shoes, etc., and the broadband seismic noise
from underground sources was the desired. The adaptive filter produced
an estimate of the noise. Instead of using the error signal (which is
normally the case) , use the adaptive filter output.
How does the adaptive filter give an estimate of the noise? Does it
require a "noise" reference?
There is no constraint on Widrow's LMS filter for the signals to be
correlated signals.
Then it would be wasting information when processing signals that are
correlated.
The constraint is that the signal and the noise
can't be correlated. The trick is to determine what is the input, what
is the reference, and how do I get the reference.
In the case where the correlation of the signals is +1 and the noise
is -1, the reference depends on what is known.
Bret Cahill- Hide quoted text -
- Show quoted text -
Bret,
What started this particular part of your thread (sorry, your thread
got a bit hijacked
with broadband noise in an adaptive filter. In the last example I
gave, the desired signal is not the correlated stuff, but the noise.
We weren't exactly addressing the particular configuration you started
with, but it leads back to it.
If I have a boadband noise signal currupted with correlated signals,
when I remove the correlated signals, I have the wanted noise
remaining. In the case of *adaptive noise cancellation* (what Widrow
calls adaptive interference cancellation) the signal is actually the
reference, and the noise is the input to the adaptive filter. This is
the model you showed in the paper. A good analysis of this is in
Widrow's book adaptive signal processing, chapter 11 or 12 IIRC (I
think it's also in the paper he wrote with McCool, et. al.). Widrow
calls this adaptive interference cancellation, rather than adaptive
noise cancellation.
With respect to long delays, with the model you referenced, if the
signal source, S + No gets to the filter before the noise source, N1,
then the filter will not adapt (non-causal). The remedy is to place
delays in the signal line to force causality. It doesn't matter if the
delay is long.
In the paper you referenced, I believe the S
be after the summation in the signal line. The signal is corrupted
with noise from N1
unknown impulse response to become No
unknown impulse response so that the sample of noise available, N1
can be used to reduce the noise level on S
problem I had. I had a seismic sensor corrupted with noise. The noise
was the seismic rumbling of trucks, cars, etc. The problem was that
the rumbling was convolved with the soil impulse response before it
got to the sensor. This is exactly the model in your reference paper,
only S
To further complicate things, the seismic sensors needed to be placed
a distance from the noise reference,
much lower SNR?
That approach may be the best thing to do in what seems like a bad
situation.
I was determining the quotient of two noisy signals, SNR > 4 - 20, in
a few seconds or one or a few cycles with an accuracy of 99.5% half
the time.
The 2 signals w/o the noise correlate 100% and the noise in one signal
correlates by negative 1 to the noise in the other signal.
The factor to multiply one signal so that that signal has the exact
negative of the noise in the other signal is known so it's easy to
create a noise free reference by adding one signal to the other signal
times that factor.
Then you can use match filtering or, if you have the time, phase
sensitive rectification to get the magnitudes.
Bret Cahill
F
Fred Marshall
Guest
On 9/15/2011 11:49 AM, maury wrote:
different? If there's a delay then one has to deal with it .. so that's
fine. I'm missing something here it seems.
It seems that I've said that one can't remove uncorrelated noise and
you've said that one can remove correlated noise. We're both correct.
Fred
That's an ANC .. the noise that's removed is correlated. What'sonly S
different? If there's a delay then one has to deal with it .. so that's
fine. I'm missing something here it seems.
It seems that I've said that one can't remove uncorrelated noise and
you've said that one can remove correlated noise. We're both correct.
Fred