Adaptive Filter Reference Constructed From the 2 Noisy Signals To Be Filtered

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


Bret Cahill

On 09/09/2011 02:50 PM, Bret Cahill wrote:
> Is this situation/solution common?  There is at least one example in
> electronics.
>
>
> Bret Cahill
>
>

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

On 9/9/2011 11:50 AM, Bret Cahill wrote:
> 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.

Fred

> > 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

On Sep 10, 10:22&#4294967295;am, Bret Cahill <BretCah...@peoplepc.com> wrote:
> > > Is this situation/solution common? &#4294967295;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? &#4294967295;
>
> 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. &#4294967295;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. &#4294967295;This is called the "reference".
>
> > Then, the reference is filtered so that the difference between that and
> > the signal of interest is minimized. &#4294967295;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.


Hardy

> 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

> > > > 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.

I forgot to add that both clean signals correlate by +1.

> > > 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.

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

> > > 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.

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

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