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

On 9/19/2011 1:48 PM, Bret Cahill wrote:
>>>>>>>> Is this situation/solution common?
>>
>>>>>>> In one situation the two clean signals correlate by +1 and the noise
>>>>>>> in the 2 signals correlate by negative 1.
>>
>>>>>>> A clean reference, therefore, can be derived by adding one noisy
>>>>>>> signal to some factor times the other noisy signal.
>>
>>>>>>>> There is at least one example in
>>>>>>>> electronics.
>>
>>>>>>> You have the voltage signal between 2 inductors and the first
>>>>>>> derivative of current signal.
>>
>>>>>>> The driving voltage is between the known inductor and ground and the
>>>>>>> noise voltage is between the unknown inductor and ground.
>>
>>>>>>> If you want to determine the unknown inductance by taking the quotient
>>>>>>> of V/(di/dt) then the noise will be worse in the quotient than the
>>>>>>> noise in the worst signal.
>>
>>>>>>> The reference allows for match filtering of the signals, however.
>>
>>>>>>> This is new in at least one application.  The question is if it is new
>>>>>>> for _any_ application.
>>
>>>>>>> Bret Cahill
>>
>>>>>> Bret,
>>
>>>>>> I will try to translate the essence of your question for my own clarity:
>>
>>>>>> You have, in concept, S1 and S2, the two "clean" signals.
>>>>>> You have, in concept, N1 and N2, the two "noises".
>>>>>> You have in realitiy, S1 + N1 and S2 + N2 ... is that right?
>>
>>>>> This is a pretty system so we can cut right to the chase.
>>
>>>>> Transducer 1 puts out S1 + N1 and, by the way the system behaves,
>>>>> transducer 2 puts out mS1 - m1N1.
>>
>>>>> where
>>
>>>>> m1 = known constant
>>>>> m = unknown const. to be determined.
>>
>>>>> For noise free signals just take the quotient of the signal from
>>>>> transducer 2 divided by transducer 1.  If this is done in real time
>>>>> then there may be zero crossings issues.  If both signals are
>>>>> rectified and integrated, however, you get a nice average of m over
>>>>> just a fraction of a cycle.
>>
>>>>> Adding noise to the signals, however, introduces an error to m.  The
>>>>> when the noise in transducer 2 causes the numerator to err high the
>>>>> noise in transducer 1 causes the denominator to err low.  The noise is
>>>>> therefore magnified in the quotient by a greater % than in either raw
>>>>> signal alone.
>>
>>>>> The noise is in the same band as the signal so some kind of adaptive
>>>>> filtering is desired.
>>
>>>>> A noise free reference is readily available simply by multiplying the
>>>>> signal from transducer 1 by m1 and then adding that to the output from
>>>>> transducer 2.
>>
>>>>> reference = m1(S1 + N1) + mS1 - m1N1 = S1(m1+ m)
>>
>>>>> There may be a phase angle between the signals which isn't an issue
>>>>> with match filtering.
>>
>>>>> The signals from the transducers do not need to be sinusoidal or even
>>>>> periodic.
>>
>>>>> The SNR is pretty high anyway, 4 - 20, so the filtering only needs to
>>>>> reduce the noise by a factor of 5 - 20 in most cases for 99.5%
>>>>> accuracy.
>>
>>>>> Bret Cahill
>>
>>>> OK.  Thanks for clarifying.
>>
>>> It may have gotten lost somewhere but both noisy signals from both
>>> transducers are filtered the same way with the same reference.
>>
>>> After that and then rectification and smoothing, the quotient is
>>> taken.
>>
>>>> Other than frequency and phase considerations, this looks a lot like an
>>>> adaptive noise canceller with a single coefficient to be adjusted.
>>
>>>> To keep things more or less standard, I'd not add noise one place and
>>>> subtract it another as long as there's a coefficient to deal with it.
>>>> I'd use S + N in all cases.
>>
>>>> So S + N1
>>>> and mS + m1N1
>>
>>> If those are the two noisy signals from the 2 transducers, then the +
>>> sign on one of the noise terms needs to be negative.
>>
>>> Also, are we dropping the subscript to N?  S as well as N don't really
>>> need one.
>>
>>>> You put mS1 - m1N1 into the direct input (i.e. the input to the adaptive
>>>> filter).
>>
>>> That's just to filter the numerator.   (It looks like we're using my
>>> notation above again)
>>
>>> For the denominator the input is S1 + N1.
>>
>>>> mS + m1N1
>>
>>> If that's the output to transducer 2 then that + or the + in the other
>>> transducer would need to be negative for the -1 correlation for noise.
>>
>>>> The adaptive filter single weight adapts to m1.
>>
>>>> Then, the output of the adaptive filter is:
>>>> -m1( S1 + N1)
>>
>>>> This is subtracted from the direct input:
>>
>>>> [mS + m1N1] - [m1(S1 +N1)] = (m-m1)S1
>>
>>>> So, I think one of us got a sign wrong here.
>>>> It's a bit bothersome that S1 is multiplied by a difference but if m1 is
>>>> relatively negative in comparison to m as you've suggested then it's better.
>>
>>> m and m1 are just two unrelated positive constants with the same
>>> units.
>>
>>> Bret Cahill
>>
>> Well, I guess that's what got me.  Normally variables can be positive or
>> negative.
>
> m and m1 are constants.
>
> In the circuit problem -- which is probably academic but serves to
> illustrate how this can be used for filtering -- the goal is to
> measure an unknown inductance.
>
>> So, why not negative m1 and S+N type notation?
>
> Inductance is always positive.  It's best to keep everything kosher.
> Going to a negative inductance may work in some cases but it could
> introduce problems down the road.
>
>> Denominator?  Where'd that come from?
>
> The only purpose is to get an accurate measurement of inductance.  One
> sensor measures voltage and the other current.
>
> Taking the quotient of voltage / di/dt = inductance.
>
> where:
>
> di/dt = the 1st derivative of current
>
> That's where the denominator comes from.
>
> So filtering the noise in both signals with the ref
>
> inductance =  (voltage * ref)/((di/dt) * ref)
>
> where * represents match filtering (multiplication in the frequency
> domain) or phase sensitive rectification.
>
> Any scalars in the ref cancel out in the quotient so there's no reason
> to worry about the magnitude of the ref.
>
> It's important to note that this is a new filtering approach only with
> respect to how the reference is created/derived.
>
>
> Bret Cahill
>
>
>
>
>
Whatever .... I wasn't addressing the inductor example because I hadn't 
got that far yet.  I was awaiting better description - as mentioned 
earlier.    So this comes as a change in the subject.  I don't think 
that limiting constants to positive values is particularly useful if it 
gets in the way of clear understanding.

Fred

> >>>>>>>> Is this situation/solution common?
>
> >>>>>>> In one situation the two clean signals correlate by +1 and the no=
ise
> >>>>>>> in the 2 signals correlate by negative 1.
>
> >>>>>>> A clean reference, therefore, can be derived by adding one noisy
> >>>>>>> signal to some factor times the other noisy signal.
>
> >>>>>>>> There is at least one example in
> >>>>>>>> electronics.
>
> >>>>>>> You have the voltage signal between 2 inductors and the first
> >>>>>>> derivative of current signal.
>
> >>>>>>> The driving voltage is between the known inductor and ground and =
the
> >>>>>>> noise voltage is between the unknown inductor and ground.
>
> >>>>>>> If you want to determine the unknown inductance by taking the quo=
tient
> >>>>>>> of V/(di/dt) then the noise will be worse in the quotient than th=
e
> >>>>>>> noise in the worst signal.
>
> >>>>>>> The reference allows for match filtering of the signals, however.
>
> >>>>>>> This is new in at least one application. =A0The question is if it=
 is new
> >>>>>>> for _any_ application.
>
> >>>>>>> Bret Cahill
>
> >>>>>> Bret,
>
> >>>>>> I will try to translate the essence of your question for my own cl=
arity:
>
> >>>>>> You have, in concept, S1 and S2, the two "clean" signals.
> >>>>>> You have, in concept, N1 and N2, the two "noises".
> >>>>>> You have in realitiy, S1 + N1 and S2 + N2 ... is that right?
>
> >>>>> This is a pretty system so we can cut right to the chase.
>
> >>>>> Transducer 1 puts out S1 + N1 and, by the way the system behaves,
> >>>>> transducer 2 puts out mS1 - m1N1.
>
> >>>>> where
>
> >>>>> m1 =3D known constant
> >>>>> m =3D unknown const. to be determined.
>
> >>>>> For noise free signals just take the quotient of the signal from
> >>>>> transducer 2 divided by transducer 1. =A0If this is done in real ti=
me
> >>>>> then there may be zero crossings issues. =A0If both signals are
> >>>>> rectified and integrated, however, you get a nice average of m over
> >>>>> just a fraction of a cycle.
>
> >>>>> Adding noise to the signals, however, introduces an error to m. =A0=
The
> >>>>> when the noise in transducer 2 causes the numerator to err high the
> >>>>> noise in transducer 1 causes the denominator to err low. =A0The noi=
se is
> >>>>> therefore magnified in the quotient by a greater % than in either r=
aw
> >>>>> signal alone.
>
> >>>>> The noise is in the same band as the signal so some kind of adaptiv=
e
> >>>>> filtering is desired.
>
> >>>>> A noise free reference is readily available simply by multiplying t=
he
> >>>>> signal from transducer 1 by m1 and then adding that to the output f=
rom
> >>>>> transducer 2.
>
> >>>>> reference =3D m1(S1 + N1) + mS1 - m1N1 =3D S1(m1+ m)
>
> >>>>> There may be a phase angle between the signals which isn't an issue
> >>>>> with match filtering.
>
> >>>>> The signals from the transducers do not need to be sinusoidal or ev=
en
> >>>>> periodic.
>
> >>>>> The SNR is pretty high anyway, 4 - 20, so the filtering only needs =
to
> >>>>> reduce the noise by a factor of 5 - 20 in most cases for 99.5%
> >>>>> accuracy.
>
> >>>>> Bret Cahill
>
> >>>> OK. =A0Thanks for clarifying.
>
> >>> It may have gotten lost somewhere but both noisy signals from both
> >>> transducers are filtered the same way with the same reference.
>
> >>> After that and then rectification and smoothing, the quotient is
> >>> taken.
>
> >>>> Other than frequency and phase considerations, this looks a lot like=
 an
> >>>> adaptive noise canceller with a single coefficient to be adjusted.
>
> >>>> To keep things more or less standard, I'd not add noise one place an=
d
> >>>> subtract it another as long as there's a coefficient to deal with it=
.
> >>>> I'd use S + N in all cases.
>
> >>>> So S + N1
> >>>> and mS + m1N1
>
> >>> If those are the two noisy signals from the 2 transducers, then the +
> >>> sign on one of the noise terms needs to be negative.
>
> >>> Also, are we dropping the subscript to N? =A0S as well as N don't rea=
lly
> >>> need one.
>
> >>>> You put mS1 - m1N1 into the direct input (i.e. the input to the adap=
tive
> >>>> filter).
>
> >>> That's just to filter the numerator. =A0 (It looks like we're using m=
y
> >>> notation above again)
>
> >>> For the denominator the input is S1 + N1.
>
> >>>> mS + m1N1
>
> >>> If that's the output to transducer 2 then that + or the + in the othe=
r
> >>> transducer would need to be negative for the -1 correlation for noise=
.
>
> >>>> The adaptive filter single weight adapts to m1.
>
> >>>> Then, the output of the adaptive filter is:
> >>>> -m1( S1 + N1)
>
> >>>> This is subtracted from the direct input:
>
> >>>> [mS + m1N1] - [m1(S1 +N1)] =3D (m-m1)S1
>
> >>>> So, I think one of us got a sign wrong here.
> >>>> It's a bit bothersome that S1 is multiplied by a difference but if m=
1 is
> >>>> relatively negative in comparison to m as you've suggested then it's=
 better.
>
> >>> m and m1 are just two unrelated positive constants with the same
> >>> units.
>
> >>> Bret Cahill
>
> >> Well, I guess that's what got me. =A0Normally variables can be positiv=
e or
> >> negative.
>
> > m and m1 are constants.
>
> > In the circuit problem -- which is probably academic but serves to
> > illustrate how this can be used for filtering -- the goal is to
> > measure an unknown inductance.
>
> >> So, why not negative m1 and S+N type notation?
>
> > Inductance is always positive. =A0It's best to keep everything kosher.
> > Going to a negative inductance may work in some cases but it could
> > introduce problems down the road.
>
> >> Denominator? =A0Where'd that come from?
>
> > The only purpose is to get an accurate measurement of inductance. =A0On=
e
> > sensor measures voltage and the other current.
>
> > Taking the quotient of voltage / di/dt =3D inductance.
>
> > where:
>
> > di/dt =3D the 1st derivative of current
>
> > That's where the denominator comes from.
>
> > So filtering the noise in both signals with the ref
>
> > inductance =3D =A0(voltage * ref)/((di/dt) * ref)
>
> > where * represents match filtering (multiplication in the frequency
> > domain) or phase sensitive rectification.
>
> > Any scalars in the ref cancel out in the quotient so there's no reason
> > to worry about the magnitude of the ref.
>
> > It's important to note that this is a new filtering approach only with
> > respect to how the reference is created/derived.
>
> > Bret Cahill
>
> Whatever .... I wasn't addressing the inductor example because I hadn't
> got that far yet. =A0 I was awaiting better description - as mentioned
> earlier. =A0 =A0

You mean a more "general" statement?

Supposing it doesn't exist?

> So this comes as a change in the subject. =A0I don't think
> that limiting constants to positive values is particularly useful if it
> gets in the way of clear understanding.

There is at least one more real world application where the constant
is always positive.

If anyone can come up with more applications, it would be most
interesting.

I've never been able to find anything like it myself.


Bret Cahill

On 9/19/2011 11:03 PM, Bret Cahill wrote:
>>>>>>>>>> Is this situation/solution common?
>>
>>>>>>>>> In one situation the two clean signals correlate by +1 and the noise
>>>>>>>>> in the 2 signals correlate by negative 1.
>>
>>>>>>>>> A clean reference, therefore, can be derived by adding one noisy
>>>>>>>>> signal to some factor times the other noisy signal.
>>
>>>>>>>>>> There is at least one example in
>>>>>>>>>> electronics.
>>
>>>>>>>>> You have the voltage signal between 2 inductors and the first
>>>>>>>>> derivative of current signal.
>>
>>>>>>>>> The driving voltage is between the known inductor and ground and the
>>>>>>>>> noise voltage is between the unknown inductor and ground.
>>
>>>>>>>>> If you want to determine the unknown inductance by taking the quotient
>>>>>>>>> of V/(di/dt) then the noise will be worse in the quotient than the
>>>>>>>>> noise in the worst signal.
>>
>>>>>>>>> The reference allows for match filtering of the signals, however.
>>
>>>>>>>>> This is new in at least one application.  The question is if it is new
>>>>>>>>> for _any_ application.
>>
>>>>>>>>> Bret Cahill
>>
>>>>>>>> Bret,
>>
>>>>>>>> I will try to translate the essence of your question for my own clarity:
>>
>>>>>>>> You have, in concept, S1 and S2, the two "clean" signals.
>>>>>>>> You have, in concept, N1 and N2, the two "noises".
>>>>>>>> You have in realitiy, S1 + N1 and S2 + N2 ... is that right?
>>
>>>>>>> This is a pretty system so we can cut right to the chase.
>>
>>>>>>> Transducer 1 puts out S1 + N1 and, by the way the system behaves,
>>>>>>> transducer 2 puts out mS1 - m1N1.
>>
>>>>>>> where
>>
>>>>>>> m1 = known constant
>>>>>>> m = unknown const. to be determined.
>>
>>>>>>> For noise free signals just take the quotient of the signal from
>>>>>>> transducer 2 divided by transducer 1.  If this is done in real time
>>>>>>> then there may be zero crossings issues.  If both signals are
>>>>>>> rectified and integrated, however, you get a nice average of m over
>>>>>>> just a fraction of a cycle.
>>
>>>>>>> Adding noise to the signals, however, introduces an error to m.  The
>>>>>>> when the noise in transducer 2 causes the numerator to err high the
>>>>>>> noise in transducer 1 causes the denominator to err low.  The noise is
>>>>>>> therefore magnified in the quotient by a greater % than in either raw
>>>>>>> signal alone.
>>
>>>>>>> The noise is in the same band as the signal so some kind of adaptive
>>>>>>> filtering is desired.
>>
>>>>>>> A noise free reference is readily available simply by multiplying the
>>>>>>> signal from transducer 1 by m1 and then adding that to the output from
>>>>>>> transducer 2.
>>
>>>>>>> reference = m1(S1 + N1) + mS1 - m1N1 = S1(m1+ m)
>>
>>>>>>> There may be a phase angle between the signals which isn't an issue
>>>>>>> with match filtering.
>>
>>>>>>> The signals from the transducers do not need to be sinusoidal or even
>>>>>>> periodic.
>>
>>>>>>> The SNR is pretty high anyway, 4 - 20, so the filtering only needs to
>>>>>>> reduce the noise by a factor of 5 - 20 in most cases for 99.5%
>>>>>>> accuracy.
>>
>>>>>>> Bret Cahill
>>
>>>>>> OK.  Thanks for clarifying.
>>
>>>>> It may have gotten lost somewhere but both noisy signals from both
>>>>> transducers are filtered the same way with the same reference.
>>
>>>>> After that and then rectification and smoothing, the quotient is
>>>>> taken.
>>
>>>>>> Other than frequency and phase considerations, this looks a lot like an
>>>>>> adaptive noise canceller with a single coefficient to be adjusted.
>>
>>>>>> To keep things more or less standard, I'd not add noise one place and
>>>>>> subtract it another as long as there's a coefficient to deal with it.
>>>>>> I'd use S + N in all cases.
>>
>>>>>> So S + N1
>>>>>> and mS + m1N1
>>
>>>>> If those are the two noisy signals from the 2 transducers, then the +
>>>>> sign on one of the noise terms needs to be negative.
>>
>>>>> Also, are we dropping the subscript to N?  S as well as N don't really
>>>>> need one.
>>
>>>>>> You put mS1 - m1N1 into the direct input (i.e. the input to the adaptive
>>>>>> filter).
>>
>>>>> That's just to filter the numerator.   (It looks like we're using my
>>>>> notation above again)
>>
>>>>> For the denominator the input is S1 + N1.
>>
>>>>>> mS + m1N1
>>
>>>>> If that's the output to transducer 2 then that + or the + in the other
>>>>> transducer would need to be negative for the -1 correlation for noise.
>>
>>>>>> The adaptive filter single weight adapts to m1.
>>
>>>>>> Then, the output of the adaptive filter is:
>>>>>> -m1( S1 + N1)
>>
>>>>>> This is subtracted from the direct input:
>>
>>>>>> [mS + m1N1] - [m1(S1 +N1)] = (m-m1)S1
>>
>>>>>> So, I think one of us got a sign wrong here.
>>>>>> It's a bit bothersome that S1 is multiplied by a difference but if m1 is
>>>>>> relatively negative in comparison to m as you've suggested then it's better.
>>
>>>>> m and m1 are just two unrelated positive constants with the same
>>>>> units.
>>
>>>>> Bret Cahill
>>
>>>> Well, I guess that's what got me.  Normally variables can be positive or
>>>> negative.
>>
>>> m and m1 are constants.
>>
>>> In the circuit problem -- which is probably academic but serves to
>>> illustrate how this can be used for filtering -- the goal is to
>>> measure an unknown inductance.
>>
>>>> So, why not negative m1 and S+N type notation?
>>
>>> Inductance is always positive.  It's best to keep everything kosher.
>>> Going to a negative inductance may work in some cases but it could
>>> introduce problems down the road.
>>
>>>> Denominator?  Where'd that come from?
>>
>>> The only purpose is to get an accurate measurement of inductance.  One
>>> sensor measures voltage and the other current.
>>
>>> Taking the quotient of voltage / di/dt = inductance.
>>
>>> where:
>>
>>> di/dt = the 1st derivative of current
>>
>>> That's where the denominator comes from.
>>
>>> So filtering the noise in both signals with the ref
>>
>>> inductance =  (voltage * ref)/((di/dt) * ref)
>>
>>> where * represents match filtering (multiplication in the frequency
>>> domain) or phase sensitive rectification.
>>
>>> Any scalars in the ref cancel out in the quotient so there's no reason
>>> to worry about the magnitude of the ref.
>>
>>> It's important to note that this is a new filtering approach only with
>>> respect to how the reference is created/derived.
>>
>>> Bret Cahill
>>
>> Whatever .... I wasn't addressing the inductor example because I hadn't
>> got that far yet.   I was awaiting better description - as mentioned
>> earlier.
>
> You mean a more "general" statement?
>
> Supposing it doesn't exist?
>
>> So this comes as a change in the subject.  I don't think
>> that limiting constants to positive values is particularly useful if it
>> gets in the way of clear understanding.
>
> There is at least one more real world application where the constant
> is always positive.
>
> If anyone can come up with more applications, it would be most
> interesting.
>
> I've never been able to find anything like it myself.
>
>
> Bret Cahill
>
>
>
>
Well, I was viewing it as a coefficient in an equation.  If the 
coefficient has to be positive then so be it.  But the math doesn't 
require it.  I still prefer S + N as a general form which can be 
extended to mS1 + m1N1.
m and m1 are coefficients which might be positive or negative.

I did ask very specific questions about the inductor model and didn't 
get any answers.  I'm still unclear what the schematic / circuit diagram 
is / was intended to be.  So I still can't comment....

Fred

> >>>>>>>>>> Is this situation/solution common?
>
> >>>>>>>>> In one situation the two clean signals correlate by +1 and the =
noise
> >>>>>>>>> in the 2 signals correlate by negative 1.
>
> >>>>>>>>> A clean reference, therefore, can be derived by adding one nois=
y
> >>>>>>>>> signal to some factor times the other noisy signal.
>
> >>>>>>>>>> There is at least one example in
> >>>>>>>>>> electronics.
>
> >>>>>>>>> You have the voltage signal between 2 inductors and the first
> >>>>>>>>> derivative of current signal.
>
> >>>>>>>>> The driving voltage is between the known inductor and ground an=
d the
> >>>>>>>>> noise voltage is between the unknown inductor and ground.
>
> >>>>>>>>> If you want to determine the unknown inductance by taking the q=
uotient
> >>>>>>>>> of V/(di/dt) then the noise will be worse in the quotient than =
the
> >>>>>>>>> noise in the worst signal.
>
> >>>>>>>>> The reference allows for match filtering of the signals, howeve=
r.
>
> >>>>>>>>> This is new in at least one application. =A0The question is if =
it is new
> >>>>>>>>> for _any_ application.
>
> >>>>>>>>> Bret Cahill
>
> >>>>>>>> Bret,
>
> >>>>>>>> I will try to translate the essence of your question for my own =
clarity:
>
> >>>>>>>> You have, in concept, S1 and S2, the two "clean" signals.
> >>>>>>>> You have, in concept, N1 and N2, the two "noises".
> >>>>>>>> You have in realitiy, S1 + N1 and S2 + N2 ... is that right?
>
> >>>>>>> This is a pretty system so we can cut right to the chase.
>
> >>>>>>> Transducer 1 puts out S1 + N1 and, by the way the system behaves,
> >>>>>>> transducer 2 puts out mS1 - m1N1.
>
> >>>>>>> where
>
> >>>>>>> m1 =3D known constant
> >>>>>>> m =3D unknown const. to be determined.
>
> >>>>>>> For noise free signals just take the quotient of the signal from
> >>>>>>> transducer 2 divided by transducer 1. =A0If this is done in real =
time
> >>>>>>> then there may be zero crossings issues. =A0If both signals are
> >>>>>>> rectified and integrated, however, you get a nice average of m ov=
er
> >>>>>>> just a fraction of a cycle.
>
> >>>>>>> Adding noise to the signals, however, introduces an error to m. =
=A0The
> >>>>>>> when the noise in transducer 2 causes the numerator to err high t=
he
> >>>>>>> noise in transducer 1 causes the denominator to err low. =A0The n=
oise is
> >>>>>>> therefore magnified in the quotient by a greater % than in either=
 raw
> >>>>>>> signal alone.
>
> >>>>>>> The noise is in the same band as the signal so some kind of adapt=
ive
> >>>>>>> filtering is desired.
>
> >>>>>>> A noise free reference is readily available simply by multiplying=
 the
> >>>>>>> signal from transducer 1 by m1 and then adding that to the output=
 from
> >>>>>>> transducer 2.
>
> >>>>>>> reference =3D m1(S1 + N1) + mS1 - m1N1 =3D S1(m1+ m)
>
> >>>>>>> There may be a phase angle between the signals which isn't an iss=
ue
> >>>>>>> with match filtering.
>
> >>>>>>> The signals from the transducers do not need to be sinusoidal or =
even
> >>>>>>> periodic.
>
> >>>>>>> The SNR is pretty high anyway, 4 - 20, so the filtering only need=
s to
> >>>>>>> reduce the noise by a factor of 5 - 20 in most cases for 99.5%
> >>>>>>> accuracy.
>
> >>>>>>> Bret Cahill
>
> >>>>>> OK. =A0Thanks for clarifying.
>
> >>>>> It may have gotten lost somewhere but both noisy signals from both
> >>>>> transducers are filtered the same way with the same reference.
>
> >>>>> After that and then rectification and smoothing, the quotient is
> >>>>> taken.
>
> >>>>>> Other than frequency and phase considerations, this looks a lot li=
ke an
> >>>>>> adaptive noise canceller with a single coefficient to be adjusted.
>
> >>>>>> To keep things more or less standard, I'd not add noise one place =
and
> >>>>>> subtract it another as long as there's a coefficient to deal with =
it.
> >>>>>> I'd use S + N in all cases.
>
> >>>>>> So S + N1
> >>>>>> and mS + m1N1
>
> >>>>> If those are the two noisy signals from the 2 transducers, then the=
 +
> >>>>> sign on one of the noise terms needs to be negative.
>
> >>>>> Also, are we dropping the subscript to N? =A0S as well as N don't r=
eally
> >>>>> need one.
>
> >>>>>> You put mS1 - m1N1 into the direct input (i.e. the input to the ad=
aptive
> >>>>>> filter).
>
> >>>>> That's just to filter the numerator. =A0 (It looks like we're using=
 my
> >>>>> notation above again)
>
> >>>>> For the denominator the input is S1 + N1.
>
> >>>>>> mS + m1N1
>
> >>>>> If that's the output to transducer 2 then that + or the + in the ot=
her
> >>>>> transducer would need to be negative for the -1 correlation for noi=
se.
>
> >>>>>> The adaptive filter single weight adapts to m1.
>
> >>>>>> Then, the output of the adaptive filter is:
> >>>>>> -m1( S1 + N1)
>
> >>>>>> This is subtracted from the direct input:
>
> >>>>>> [mS + m1N1] - [m1(S1 +N1)] =3D (m-m1)S1
>
> >>>>>> So, I think one of us got a sign wrong here.
> >>>>>> It's a bit bothersome that S1 is multiplied by a difference but if=
 m1 is
> >>>>>> relatively negative in comparison to m as you've suggested then it=
's better.
>
> >>>>> m and m1 are just two unrelated positive constants with the same
> >>>>> units.
>
> >>>>> Bret Cahill
>
> >>>> Well, I guess that's what got me. =A0Normally variables can be posit=
ive or
> >>>> negative.
>
> >>> m and m1 are constants.
>
> >>> In the circuit problem -- which is probably academic but serves to
> >>> illustrate how this can be used for filtering -- the goal is to
> >>> measure an unknown inductance.
>
> >>>> So, why not negative m1 and S+N type notation?
>
> >>> Inductance is always positive. =A0It's best to keep everything kosher=
.
> >>> Going to a negative inductance may work in some cases but it could
> >>> introduce problems down the road.
>
> >>>> Denominator? =A0Where'd that come from?
>
> >>> The only purpose is to get an accurate measurement of inductance. =A0=
One
> >>> sensor measures voltage and the other current.
>
> >>> Taking the quotient of voltage / di/dt =3D inductance.
>
> >>> where:
>
> >>> di/dt =3D the 1st derivative of current
>
> >>> That's where the denominator comes from.
>
> >>> So filtering the noise in both signals with the ref
>
> >>> inductance =3D =A0(voltage * ref)/((di/dt) * ref)
>
> >>> where * represents match filtering (multiplication in the frequency
> >>> domain) or phase sensitive rectification.
>
> >>> Any scalars in the ref cancel out in the quotient so there's no reaso=
n
> >>> to worry about the magnitude of the ref.
>
> >>> It's important to note that this is a new filtering approach only wit=
h
> >>> respect to how the reference is created/derived.
>
> >>> Bret Cahill
>
> >> Whatever .... I wasn't addressing the inductor example because I hadn'=
t
> >> got that far yet. =A0 I was awaiting better description - as mentioned
> >> earlier.
>
> > You mean a more "general" statement?
>
> > Supposing it doesn't exist?
>
> >> So this comes as a change in the subject. =A0I don't think
> >> that limiting constants to positive values is particularly useful if i=
t
> >> gets in the way of clear understanding.
>
> > There is at least one more real world application where the constant
> > is always positive.
>
> > If anyone can come up with more applications, it would be most
> > interesting.
>
> > I've never been able to find anything like it myself.
>
> > Bret Cahill
>
> Well, I was viewing it as a coefficient in an equation. =A0

Equations aren't created in a vacuum.  They generally come from
somewhere.

> If the
> coefficient has to be positive then so be it. =A0But the math doesn't
> require it. =A0I still prefer S + N as a general form which can be
> extended to mS1 + m1N1.
> m and m1 are coefficients which might be positive or negative.
>
> I did ask very specific questions about the inductor model and didn't
> get any answers. =A0I'm still unclear what the schematic / circuit diagra=
m
> is / was intended to be. =A0So I still can't comment....

Very simple.  Two inductors in series.  An unknown signal driving
voltage is between the known inductance, L1 and ground.

And an unknown noise generating voltage is between the unknown
inductor, L, and ground.

Both voltages fluctuate aperiodically with some overlap in band width.

The 2 transducers measure,

1.  voltage, V, between the node between the two inductors, and,

2.  current, i, in the circuit.

To determine the unknown inductance just divide V by the 1st
derivative of current, di/dt.

To filter the noise create the reference, V + L1 * ( di/dt) which
equals the driving voltage and then use it to match filter or PSR both
signals.


Bret Cahill

On 9/20/2011 11:10 PM, Bret Cahill wrote:
>>>>>>>>>>>> Is this situation/solution common?
>>
>>>>>>>>>>> In one situation the two clean signals correlate by +1 and the noise
>>>>>>>>>>> in the 2 signals correlate by negative 1.
>>
>>>>>>>>>>> A clean reference, therefore, can be derived by adding one noisy
>>>>>>>>>>> signal to some factor times the other noisy signal.
>>
>>>>>>>>>>>> There is at least one example in
>>>>>>>>>>>> electronics.
>>
>>>>>>>>>>> You have the voltage signal between 2 inductors and the first
>>>>>>>>>>> derivative of current signal.
>>
>>>>>>>>>>> The driving voltage is between the known inductor and ground and the
>>>>>>>>>>> noise voltage is between the unknown inductor and ground.
>>
>>>>>>>>>>> If you want to determine the unknown inductance by taking the quotient
>>>>>>>>>>> of V/(di/dt) then the noise will be worse in the quotient than the
>>>>>>>>>>> noise in the worst signal.
>>
>>>>>>>>>>> The reference allows for match filtering of the signals, however.
>>
>>>>>>>>>>> This is new in at least one application.  The question is if it is new
>>>>>>>>>>> for _any_ application.
>>
>>>>>>>>>>> Bret Cahill
>>
>>>>>>>>>> Bret,
>>
>>>>>>>>>> I will try to translate the essence of your question for my own clarity:
>>
>>>>>>>>>> You have, in concept, S1 and S2, the two "clean" signals.
>>>>>>>>>> You have, in concept, N1 and N2, the two "noises".
>>>>>>>>>> You have in realitiy, S1 + N1 and S2 + N2 ... is that right?
>>
>>>>>>>>> This is a pretty system so we can cut right to the chase.
>>
>>>>>>>>> Transducer 1 puts out S1 + N1 and, by the way the system behaves,
>>>>>>>>> transducer 2 puts out mS1 - m1N1.
>>
>>>>>>>>> where
>>
>>>>>>>>> m1 = known constant
>>>>>>>>> m = unknown const. to be determined.
>>
>>>>>>>>> For noise free signals just take the quotient of the signal from
>>>>>>>>> transducer 2 divided by transducer 1.  If this is done in real time
>>>>>>>>> then there may be zero crossings issues.  If both signals are
>>>>>>>>> rectified and integrated, however, you get a nice average of m over
>>>>>>>>> just a fraction of a cycle.
>>
>>>>>>>>> Adding noise to the signals, however, introduces an error to m.  The
>>>>>>>>> when the noise in transducer 2 causes the numerator to err high the
>>>>>>>>> noise in transducer 1 causes the denominator to err low.  The noise is
>>>>>>>>> therefore magnified in the quotient by a greater % than in either raw
>>>>>>>>> signal alone.
>>
>>>>>>>>> The noise is in the same band as the signal so some kind of adaptive
>>>>>>>>> filtering is desired.
>>
>>>>>>>>> A noise free reference is readily available simply by multiplying the
>>>>>>>>> signal from transducer 1 by m1 and then adding that to the output from
>>>>>>>>> transducer 2.
>>
>>>>>>>>> reference = m1(S1 + N1) + mS1 - m1N1 = S1(m1+ m)
>>
>>>>>>>>> There may be a phase angle between the signals which isn't an issue
>>>>>>>>> with match filtering.
>>
>>>>>>>>> The signals from the transducers do not need to be sinusoidal or even
>>>>>>>>> periodic.
>>
>>>>>>>>> The SNR is pretty high anyway, 4 - 20, so the filtering only needs to
>>>>>>>>> reduce the noise by a factor of 5 - 20 in most cases for 99.5%
>>>>>>>>> accuracy.
>>
>>>>>>>>> Bret Cahill
>>
>>>>>>>> OK.  Thanks for clarifying.
>>
>>>>>>> It may have gotten lost somewhere but both noisy signals from both
>>>>>>> transducers are filtered the same way with the same reference.
>>
>>>>>>> After that and then rectification and smoothing, the quotient is
>>>>>>> taken.
>>
>>>>>>>> Other than frequency and phase considerations, this looks a lot like an
>>>>>>>> adaptive noise canceller with a single coefficient to be adjusted.
>>
>>>>>>>> To keep things more or less standard, I'd not add noise one place and
>>>>>>>> subtract it another as long as there's a coefficient to deal with it.
>>>>>>>> I'd use S + N in all cases.
>>
>>>>>>>> So S + N1
>>>>>>>> and mS + m1N1
>>
>>>>>>> If those are the two noisy signals from the 2 transducers, then the +
>>>>>>> sign on one of the noise terms needs to be negative.
>>
>>>>>>> Also, are we dropping the subscript to N?  S as well as N don't really
>>>>>>> need one.
>>
>>>>>>>> You put mS1 - m1N1 into the direct input (i.e. the input to the adaptive
>>>>>>>> filter).
>>
>>>>>>> That's just to filter the numerator.   (It looks like we're using my
>>>>>>> notation above again)
>>
>>>>>>> For the denominator the input is S1 + N1.
>>
>>>>>>>> mS + m1N1
>>
>>>>>>> If that's the output to transducer 2 then that + or the + in the other
>>>>>>> transducer would need to be negative for the -1 correlation for noise.
>>
>>>>>>>> The adaptive filter single weight adapts to m1.
>>
>>>>>>>> Then, the output of the adaptive filter is:
>>>>>>>> -m1( S1 + N1)
>>
>>>>>>>> This is subtracted from the direct input:
>>
>>>>>>>> [mS + m1N1] - [m1(S1 +N1)] = (m-m1)S1
>>
>>>>>>>> So, I think one of us got a sign wrong here.
>>>>>>>> It's a bit bothersome that S1 is multiplied by a difference but if m1 is
>>>>>>>> relatively negative in comparison to m as you've suggested then it's better.
>>
>>>>>>> m and m1 are just two unrelated positive constants with the same
>>>>>>> units.
>>
>>>>>>> Bret Cahill
>>
>>>>>> Well, I guess that's what got me.  Normally variables can be positive or
>>>>>> negative.
>>
>>>>> m and m1 are constants.
>>
>>>>> In the circuit problem -- which is probably academic but serves to
>>>>> illustrate how this can be used for filtering -- the goal is to
>>>>> measure an unknown inductance.
>>
>>>>>> So, why not negative m1 and S+N type notation?
>>
>>>>> Inductance is always positive.  It's best to keep everything kosher.
>>>>> Going to a negative inductance may work in some cases but it could
>>>>> introduce problems down the road.
>>
>>>>>> Denominator?  Where'd that come from?
>>
>>>>> The only purpose is to get an accurate measurement of inductance.  One
>>>>> sensor measures voltage and the other current.
>>
>>>>> Taking the quotient of voltage / di/dt = inductance.
>>
>>>>> where:
>>
>>>>> di/dt = the 1st derivative of current
>>
>>>>> That's where the denominator comes from.
>>
>>>>> So filtering the noise in both signals with the ref
>>
>>>>> inductance =  (voltage * ref)/((di/dt) * ref)
>>
>>>>> where * represents match filtering (multiplication in the frequency
>>>>> domain) or phase sensitive rectification.
>>
>>>>> Any scalars in the ref cancel out in the quotient so there's no reason
>>>>> to worry about the magnitude of the ref.
>>
>>>>> It's important to note that this is a new filtering approach only with
>>>>> respect to how the reference is created/derived.
>>
>>>>> Bret Cahill
>>
>>>> Whatever .... I wasn't addressing the inductor example because I hadn't
>>>> got that far yet.   I was awaiting better description - as mentioned
>>>> earlier.
>>
>>> You mean a more "general" statement?
>>
>>> Supposing it doesn't exist?
>>
>>>> So this comes as a change in the subject.  I don't think
>>>> that limiting constants to positive values is particularly useful if it
>>>> gets in the way of clear understanding.
>>
>>> There is at least one more real world application where the constant
>>> is always positive.
>>
>>> If anyone can come up with more applications, it would be most
>>> interesting.
>>
>>> I've never been able to find anything like it myself.
>>
>>> Bret Cahill
>>
>> Well, I was viewing it as a coefficient in an equation.
>
> Equations aren't created in a vacuum.  They generally come from
> somewhere.
>
>> If the
>> coefficient has to be positive then so be it.  But the math doesn't
>> require it.  I still prefer S + N as a general form which can be
>> extended to mS1 + m1N1.
>> m and m1 are coefficients which might be positive or negative.
>>
>> I did ask very specific questions about the inductor model and didn't
>> get any answers.  I'm still unclear what the schematic / circuit diagram
>> is / was intended to be.  So I still can't comment....
>
> Very simple.  Two inductors in series.  An unknown signal driving
> voltage is between the known inductance, L1 and ground.
>
> And an unknown noise generating voltage is between the unknown
> inductor, L, and ground.

Which end of the inductor? Is the other end grounded?

> Both voltages fluctuate aperiodically with some overlap in band width.
>
> The 2 transducers measure,
>
> 1.  voltage, V, between the node between the two inductors, and,
>
> 2.  current, i, in the circuit.
>
> To determine the unknown inductance just divide V by the 1st
> derivative of current, di/dt.
>
> To filter the noise create the reference, V + L1 * ( di/dt) which
> equals the driving voltage and then use it to match filter or PSR both
> signals.

If the noises aren't from the same source, they don't correlate at all.

Jerry
-- 
Engineering is the art of making what you want from things you can get.

> > >>>>>>>>>> Is this situation/solution common?
>
> > >>>>>>>>> In one situation the two clean signals correlate by +1 and the noise
> > >>>>>>>>> in the 2 signals correlate by negative 1.
>
> > >>>>>>>>> A clean reference, therefore, can be derived by adding one noisy
> > >>>>>>>>> signal to some factor times the other noisy signal.
>
> > >>>>>>>>>> There is at least one example in
> > >>>>>>>>>> electronics.
>
> > >>>>>>>>> You have the voltage signal between 2 inductors and the first
> > >>>>>>>>> derivative of current signal.
>
> > >>>>>>>>> The driving voltage is between the known inductor and ground and the
> > >>>>>>>>> noise voltage is between the unknown inductor and ground.
>
> > >>>>>>>>> If you want to determine the unknown inductance by taking the quotient
> > >>>>>>>>> of V/(di/dt) then the noise will be worse in the quotient than the
> > >>>>>>>>> noise in the worst signal.
>
> > >>>>>>>>> The reference allows for match filtering of the signals, however.
>
> > >>>>>>>>> This is new in at least one application. �The question is if it is new
> > >>>>>>>>> for _any_ application.
>
> > >>>>>>>>> Bret Cahill
>
> > >>>>>>>> Bret,
>
> > >>>>>>>> I will try to translate the essence of your question for my own clarity:
>
> > >>>>>>>> You have, in concept, S1 and S2, the two "clean" signals.
> > >>>>>>>> You have, in concept, N1 and N2, the two "noises".
> > >>>>>>>> You have in realitiy, S1 + N1 and S2 + N2 ... is that right?
>
> > >>>>>>> This is a pretty system so we can cut right to the chase.
>
> > >>>>>>> Transducer 1 puts out S1 + N1 and, by the way the system behaves,
> > >>>>>>> transducer 2 puts out mS1 - m1N1.
>
> > >>>>>>> where
>
> > >>>>>>> m1 = known constant
> > >>>>>>> m = unknown const. to be determined.
>
> > >>>>>>> For noise free signals just take the quotient of the signal from
> > >>>>>>> transducer 2 divided by transducer 1. �If this is done in real time
> > >>>>>>> then there may be zero crossings issues. �If both signals are
> > >>>>>>> rectified and integrated, however, you get a nice average of m over
> > >>>>>>> just a fraction of a cycle.
>
> > >>>>>>> Adding noise to the signals, however, introduces an error to m. �The
> > >>>>>>> when the noise in transducer 2 causes the numerator to err high the
> > >>>>>>> noise in transducer 1 causes the denominator to err low. �The noise is
> > >>>>>>> therefore magnified in the quotient by a greater % than in either raw
> > >>>>>>> signal alone.
>
> > >>>>>>> The noise is in the same band as the signal so some kind of adaptive
> > >>>>>>> filtering is desired.
>
> > >>>>>>> A noise free reference is readily available simply by multiplying the
> > >>>>>>> signal from transducer 1 by m1 and then adding that to the output from
> > >>>>>>> transducer 2.
>
> > >>>>>>> reference = m1(S1 + N1) + mS1 - m1N1 = S1(m1+ m)
>
> > >>>>>>> There may be a phase angle between the signals which isn't an issue
> > >>>>>>> with match filtering.
>
> > >>>>>>> The signals from the transducers do not need to be sinusoidal or even
> > >>>>>>> periodic.
>
> > >>>>>>> The SNR is pretty high anyway, 4 - 20, so the filtering only needs to
> > >>>>>>> reduce the noise by a factor of 5 - 20 in most cases for 99.5%
> > >>>>>>> accuracy.
>
> > >>>>>>> Bret Cahill
>
> > >>>>>> OK. �Thanks for clarifying.
>
> > >>>>> It may have gotten lost somewhere but both noisy signals from both
> > >>>>> transducers are filtered the same way with the same reference.
>
> > >>>>> After that and then rectification and smoothing, the quotient is
> > >>>>> taken.
>
> > >>>>>> Other than frequency and phase considerations, this looks a lot like an
> > >>>>>> adaptive noise canceller with a single coefficient to be adjusted.
>
> > >>>>>> To keep things more or less standard, I'd not add noise one place and
> > >>>>>> subtract it another as long as there's a coefficient to deal with it.
> > >>>>>> I'd use S + N in all cases.
>
> > >>>>>> So S + N1
> > >>>>>> and mS + m1N1
>
> > >>>>> If those are the two noisy signals from the 2 transducers, then the +
> > >>>>> sign on one of the noise terms needs to be negative.
>
> > >>>>> Also, are we dropping the subscript to N? �S as well as N don't really
> > >>>>> need one.
>
> > >>>>>> You put mS1 - m1N1 into the direct input (i.e. the input to the adaptive
> > >>>>>> filter).
>
> > >>>>> That's just to filter the numerator. � (It looks like we're using my
> > >>>>> notation above again)
>
> > >>>>> For the denominator the input is S1 + N1.
>
> > >>>>>> mS + m1N1
>
> > >>>>> If that's the output to transducer 2 then that + or the + in the other
> > >>>>> transducer would need to be negative for the -1 correlation for noise.
>
> > >>>>>> The adaptive filter single weight adapts to m1.
>
> > >>>>>> Then, the output of the adaptive filter is:
> > >>>>>> -m1( S1 + N1)
>
> > >>>>>> This is subtracted from the direct input:
>
> > >>>>>> [mS + m1N1] - [m1(S1 +N1)] = (m-m1)S1
>
> > >>>>>> So, I think one of us got a sign wrong here.
> > >>>>>> It's a bit bothersome that S1 is multiplied by a difference but if m1 is
> > >>>>>> relatively negative in comparison to m as you've suggested then it's better.
>
> > >>>>> m and m1 are just two unrelated positive constants with the same
> > >>>>> units.
>
> > >>>>> Bret Cahill
>
> > >>>> Well, I guess that's what got me. �Normally variables can be positive or
> > >>>> negative.
>
> > >>> m and m1 are constants.
>
> > >>> In the circuit problem -- which is probably academic but serves to
> > >>> illustrate how this can be used for filtering -- the goal is to
> > >>> measure an unknown inductance.
>
> > >>>> So, why not negative m1 and S+N type notation?
>
> > >>> Inductance is always positive. �It's best to keep everything kosher.
> > >>> Going to a negative inductance may work in some cases but it could
> > >>> introduce problems down the road.
>
> > >>>> Denominator? �Where'd that come from?
>
> > >>> The only purpose is to get an accurate measurement of inductance. �One
> > >>> sensor measures voltage and the other current.
>
> > >>> Taking the quotient of voltage / di/dt = inductance.
>
> > >>> where:
>
> > >>> di/dt = the 1st derivative of current
>
> > >>> That's where the denominator comes from.
>
> > >>> So filtering the noise in both signals with the ref
>
> > >>> inductance = �(voltage * ref)/((di/dt) * ref)
>
> > >>> where * represents match filtering (multiplication in the frequency
> > >>> domain) or phase sensitive rectification.
>
> > >>> Any scalars in the ref cancel out in the quotient so there's no reason
> > >>> to worry about the magnitude of the ref.
>
> > >>> It's important to note that this is a new filtering approach only with
> > >>> respect to how the reference is created/derived.
>
> > >>> Bret Cahill
>
> > >> Whatever .... I wasn't addressing the inductor example because I hadn't
> > >> got that far yet. � I was awaiting better description - as mentioned
> > >> earlier.
>
> > > You mean a more "general" statement?
>
> > > Supposing it doesn't exist?
>
> > >> So this comes as a change in the subject. �I don't think
> > >> that limiting constants to positive values is particularly useful if it
> > >> gets in the way of clear understanding.
>
> > > There is at least one more real world application where the constant
> > > is always positive.
>
> > > If anyone can come up with more applications, it would be most
> > > interesting.
>
> > > I've never been able to find anything like it myself.
>
> > > Bret Cahill
>
> > Well, I was viewing it as a coefficient in an equation. �
>
> Equations aren't created in a vacuum. �They generally come from
> somewhere.
>
> > If the
> > coefficient has to be positive then so be it. �But the math doesn't
> > require it. �I still prefer S + N as a general form which can be
> > extended to mS1 + m1N1.
> > m and m1 are coefficients which might be positive or negative.
>
> > I did ask very specific questions about the inductor model and didn't
> > get any answers. �I'm still unclear what the schematic / circuit diagram
> > is / was intended to be. �So I still can't comment....
>
> Very simple. �Two inductors in series. �An unknown signal driving
> voltage is between the known inductance, L1 and ground.
>
> And an unknown noise generating voltage is between the unknown
> inductor, L, and ground.
>
> Both voltages fluctuate aperiodically with some overlap in band width.
>
> The 2 transducers measure,
>
> 1. �voltage, V, between the node between the two inductors, and,
>
> 2. �current, i, in the circuit.
>
> To determine the unknown inductance just divide V by the 1st
> derivative of current, di/dt.
>
> To filter the noise create the reference, V + L1 * ( di/dt) which
> equals the driving voltage and then use it to match filter or PSR both
> signals.

The reference can be calculated in either the time or frequency
domain.

Since you have to take the Fourier transform of each signal anyway
when match filtering it saves some time to calculate the reference in
the frequency domain, 2 FTs instead of 3.


Bret Cahill

On 9/20/2011 11:10 PM, Bret Cahill wrote:

   ...

> Very simple.  Two inductors in series.  An unknown signal driving
> voltage is between the known inductance, L1 and ground.

What does "A voltage is applied between L1 and ground." mean? What are 
the ends of L1 connected to?

> And an unknown noise generating voltage is between the unknown
> inductor, L, and ground.

Hmm. The two inductors are in series. What does the circuit look like? I 
can guess, but You haven't told me yet, so I don't know. And what is a 
noise-generating voltage, anyhow?

> Both voltages fluctuate aperiodically with some overlap in band width.

But only one of them generates (induces?) noise.

> The 2 transducers measure,
>
> 1.  voltage, V, between the node between the two inductors, and,

A voltage between the node and what? Voltmeters have two leads.

> 2.  current, i, in the circuit.
>
> To determine the unknown inductance just divide V by the 1st
> derivative of current, di/dt.

No. V is RMS voltage. You want the instantaneous voltage, v. What is the 
second inductor for?

> To filter the noise create the reference, V + L1 * ( di/dt) which
> equals the driving voltage and then use it to match filter or PSR both
> signals.

What noise? v = L*di/dt whether v is noisy or not. The only noises that 
van disturb the measurement are the sensor noises. There is no hope that 
they will be correlated.

Jerry
-- 
Engineering is the art of making what you want from things you can get.

The circuit is a simple loop:

Ground -- Vs(t) -- L1 -- L -- Vn(t) -- Ground

Vs(t) is the unknown clean signal.

Vn(t) is unknown uncorrelated noise.

L(1) is the known inductor

L is the unknown inductor to be determined.

Vm(t) is the voltage measured at the node between L1 -- L and ground.
(Not shown)

i is the current in the loop.

If you know

1.  the voltmeter voltage Vm(t) measured between ground and the node
between the inductors.

2.  the current i through the loop

3.  the noise, Vn(t) = 0

then it's easy to determine L:

L = Vm(t)/(di/dt)

(except near crossings)

If Vn(t) is significant and in the same band as Vs(t) then the noise
from Vn(t) can be filtered by calculating Vs(t) as a noise free
reference:

Vs(t) = Vm(t) + L1(di/dt) = reference

For phase sensitive rectification,

Integral [Vm(t) * (Vm(t) + L1(di/dt))] / Integral [(di/dt) * (Vm(t) +
L1(di/dt))] => L


Bret Cahill

On 9/22/2011 1:05 AM, Bret Cahill wrote:
> The circuit is a simple loop:
>
> Ground -- Vs(t) -- L1 -- L -- Vn(t) -- Ground

I read that as ground -- L1 -- L -- ground, with Vs(t) and Vn(t) 
referenced to ground. Where are their other ends connected?

> Vs(t) is the unknown clean signal.
>
> Vn(t) is unknown uncorrelated noise.

Not correlated to what?

> L(1) is the known inductor

Whet use does it have?

> L is the unknown inductor to be determined.
>
> Vm(t) is the voltage measured at the node between L1 -- L and ground.
> (Not shown)

Is Vm(t) the same as Vn(t)? If not, where is it in your scheme?

> i is the current in the loop.
>
> If you know
>
> 1.  the voltmeter voltage Vm(t) measured between ground and the node
> between the inductors.

Since your circuit is a loop with two nodes (one of them ground), there 
is only one place to measure any voltage. The same voltage is across 
both L1 an L. What causes it?

> 2.  the current i through the loop
>
> 3.  the noise, Vn(t) = 0
>
> then it's easy to determine L:
>
> L = Vm(t)/(di/dt)
>
> (except near crossings)
>
> If Vn(t) is significant and in the same band as Vs(t) then the noise
> from Vn(t) can be filtered by calculating Vs(t) as a noise free
> reference:
>
> Vs(t) = Vm(t) + L1(di/dt) = reference
>
> For phase sensitive rectification,
>
> Integral [Vm(t) * (Vm(t) + L1(di/dt))] / Integral [(di/dt) * (Vm(t) +
> L1(di/dt))] =>  L

How do you measure or compute di/dt?

I wouldn't presume to tell you that you don't know what you're talking 
about. I can say with confidence that I don't know what you're talking 
about.

Jerry
-- 
Engineering is the art of making what you want from things you can get.

> > The circuit is a simple loop:
>
> > Ground -- Vs(t) -- L1 -- L -- Vn(t) -- Ground
>
> I read that as ground -- L1 -- L -- ground,

Feel free to start another thread if you want a circuit w/o voltage or
current sources.

The circuit on this thread is:

Ground -- Vs(t) -- L1 -- L -- Vn(t) -- Ground

> with Vs(t) and Vn(t)
> referenced to ground. Where are their other ends connected?

> > Vs(t) is the unknown clean signal.

> > Vn(t) is unknown uncorrelated noise.

> Not correlated to what?

You get 3 guesses and the 1st 2 don't count.

> > L(1) is the known inductor

> Whet use does it have?

1.  Some circuits have to have it.

2.  Without it then Vm(t) would = Vs(t) which may be more expensive
and less accurate to measure than with L1.

3.  When Vm(t) = Vs(t) then Vm(t) does not need to be filtered and it
can be used a reference to filter di/dt but this isn't as interesting
as with L1 in the circuit.

> > L is the unknown inductor to be determined.

> > Vm(t) is the voltage measured at the node between L1 -- L and ground.
> > (Not shown)

> Is Vm(t) the same as Vn(t)?

Not as long as L1 is between the 2 voltages.

>  If not, where is it in your scheme?

Vm(t) is measured between ground and the node between the two
inductors

> > i is the current in the loop.
>
> > If you know
>
> > 1. �the voltmeter voltage Vm(t) measured between ground and the node
> > between the inductors.
>
> Since your circuit is a loop with two nodes (one of them ground), there
> is only one place to measure any voltage.

You think the entire circuit is at 1 voltage?

> The same voltage is across
> both L1 an L.

Do you mean the same voltage _drop_?  The voltage drop over each
inductors will generally be different.

> What causes it?

It's plugged into something.

> > 2. �the current i through the loop
>
> > 3. �the noise, Vn(t) = 0
>
> > then it's easy to determine L:
>
> > L = Vm(t)/(di/dt)
>
> > (except near crossings)
>
> > If Vn(t) is significant and in the same band as Vs(t) then the noise
> > from Vn(t) can be filtered by calculating Vs(t) as a noise free
> > reference:
>
> > Vs(t) = Vm(t) + L1(di/dt) = reference
>
> > For phase sensitive rectification,
>
> > Integral [Vm(t) * (Vm(t) + L1(di/dt))] / Integral [(di/dt) * (Vm(t) +
> > L1(di/dt))] => �L
>
> How do you measure or compute di/dt?

Analog or digital?


Bret Cahill