Adaptive Filter Reference Constructed From the 2 Noisy Signa

Is this situation/solution common? There is at least one example in
electronics.


Bret Cahill

Is this situation/solution common? There is at least one example in
electronics.


Bret Cahill

Is this situation/solution common?  There is at least one example in
electronics.

Bret Cahill

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.

Is this situation/solution common?  There is at least one example in
electronics.

Bret Cahill

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?  

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.

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?

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.



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.

I'll check it out.

Bret Cahill

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".

Is this situation/solution common?  There is at least one example in
electronics.

Bret Cahill

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?  

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.

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?

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.

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.

I'll check it out.

Bret Cahill

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.

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"..

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.

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".

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.

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.

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".

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

On 9/9/2011 4:13 PM, Bret Cahill wrote:





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".

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

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- Hide quoted text -

- Show quoted text -

On Sep 14, 1:58 am, Fred Marshall<fmarshallxremove_th...@acm.org
wrote:
On 9/9/2011 4:13 PM, Bret Cahill wrote:





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".

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

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- Hide quoted text -

- Show quoted text -

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

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".

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

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- Hide quoted text -

- Show quoted text -

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

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?

On 9/14/2011 9:21 AM, maury wrote:





On Sep 14, 1:58 am, Fred Marshall<fmarshallxremove_th...@acm.org
wrote:
On 9/9/2011 4:13 PM, Bret Cahill wrote:

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".

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

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- Hide quoted text -

- Show quoted text -

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

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- Hide quoted text -

- Show quoted text -

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.