Adaptive Filter Reference Constructed From the 2 Noisy Signa

[Bret Cahill]

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

 

[Fred Marshall]

On 9/22/2011 4:30 PM, Bret Cahill wrote:

Do you have any comments or questions on the reference,

Vm(t) + L1(di/dt)

for filtering the circuit,

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

to determine the unknown inductance L,

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

I think I understand the circuit diagram now. Thank you.

Next, where did this expression of integrals come from? Its derivation
doesn't just jump out at me.

Fred

 

[Bret Cahill]

So there are more than two nodes! I need a picture.

See the three "---" lines between Vs(t) and L1 and L and Vn(t)?

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

? ? ?

Each one is generally at a different voltage.


.. . .

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?

Either way works.

Is there any reason to discuss something that has already been
invented?

Do you have any comments or questions on the reference,

Vm(t) + L1(di/dt)

for filtering the circuit,

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

to determine the unknown inductance L,

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

? ? ?


Bret Cahill

 

[Jerry Avins]

On 9/22/2011 7:30 PM, Bret Cahill wrote:

So there are more than two nodes! I need a picture.

See the three "---" lines between Vs(t) and L1 and L and Vn(t)?

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

? ? ?

Each one is generally at a different voltage.


. . .


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?

Either way works.

Is there any reason to discuss something that has already been
invented?

Do you have any comments or questions on the reference,

Vm(t) + L1(di/dt)

for filtering the circuit,

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

OK. So Vs(t) and Vn(t) are voltage generators with one end grounded.
Presumably, Vs(t) can have a very high SNR. Moreover, there are four
nodes, and L and L! form an inductive voltage divider. Why is noise a
problem? Are the inductances very small? Why not simply short out Vn(t)?

to determine the unknown inductance L,

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

There is no need to differentiate. The ratio of the voltages across the
inductors is the ratio of the inductances.

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

 

[Bret Cahill]

Do you have any comments or questions on the reference,

Vm(t) + L1(di/dt)

for filtering the circuit,

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

to determine the unknown inductance L,

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

I think I understand the circuit diagram now.  Thank you.

Next, where did this expression of integrals come from?  Its derivation
doesn't just jump out at me.

Phase sensitive rectification.

Multiply the noisy signal by the noise free reference and to then
integrate or otherwise low pass filter.

The clean part of the signal correlates with the reference and
increases with the integration time. The noise part of the signal
doesn't correlate with the reference eventually disappears as a
percentage of the integral value.

PSR both Vm(t) and di/dt over the same time t and then take the
quotient to get the unknown inductor L.

If no one has ever derived a reference like this before now it is
understandable since it's so easy to get Vs(t) and, for that matter,
inductance.


Bret Cahill

 

[Fred Marshall]

On 9/22/2011 7:02 PM, Bret Cahill wrote:

Phase sensitive rectification.

Oh cripes and here I thought we were talking about adaptive filters.

But, I've noticed you mentioned matched filters along the way .. I
wasn't "getting it".

I wouldn't generally associate the two directly. Maybe a good Master's
thesis topic:

"The Relationship Between Adaptive Filters and Matched Filters"

But, somehow I think the answer is trivial .. according to my notion of
what those two things are:

- A Matched Filter is one that is matched to a KNOWN signal and outputs
the best SNR in the presence of white Gaussian noise.

- An Adaptive Filter is one that attempts to either remove noise (by
some definition) in the form of an ANC or ALE - one with a noise
reference and one without in their simplest forms. AND is capable of
changing in dynamic conditions of signal and noise.

I suppose if the signal is stable and the noise is white Gaussian then
an ALE may tend to the matched filter. But I don't' think I know that
for sure. And, an ANC will simply shut off and not do anything with
that kind of noise.

But "Phase Senssitive Rectification"? Where did that come from in this
context?

Fred

 

[Bret Cahill]

The noise free reference,

Vm(t) + L1(di/dt)

for filtering the circuit,

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

is used to determine the unknown inductance L,

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

Phase sensitive rectification.

Oh cripes and here I thought we were talking about adaptive filters.

Well?

Could any adaptive filter be made to work with the reference above?

But, I've noticed you mentioned matched filters along the way .. I
wasn't "getting it".

I wouldn't generally associate the two directly.  Maybe a good Master's
thesis topic:

"The Relationship Between Adaptive Filters and Matched Filters"

What about,

"Various Categorizations of Reference Based Filters"

But, somehow I think the answer is trivial .. according to my notion of
what those two things are:

- A Matched Filter is one that is matched to a KNOWN signal and outputs
the best SNR in the presence of white Gaussian noise.

Try match filtering a noisy signal using the reference above, Vm(t) +
L1(di/dt) to determine L and compare it with PSR.

Try both filters using the same signal, same noise and the same
reference.

You can do everything on Excel.

To save time construct the reference in the frequency domain.

- An Adaptive Filter is one that attempts to either remove noise (by
some definition) in the form of an ANC or ALE - one with a noise
reference and one without in their simplest forms.  AND is capable of
changing in dynamic conditions of signal and noise.

I suppose if the signal is stable and the noise is white Gaussian then
an ALE may tend to the matched filter.  But I don't' think I know that
for sure.  And, an ANC will simply shut off and not do anything with
that kind of noise.

But "Phase Senssitive Rectification"?  Where did that come from in this
context?

The question is if an accurate determination of L could be
accomplished using another reference with _any_ filter.

So far the answer seems to be "no."


Bret Cahill

 

[Bret Cahill]

So there are more than two nodes! I need a picture.

See the three "---" lines between Vs(t) and L1 and L and  Vn(t)?

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

?  ?  ?

Each one is generally at a different voltage.

. . .

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?

Either way works.

Is there any reason to discuss something that has already been
invented?

Do you have any comments or questions on the reference,

Vm(t) + L1(di/dt)

for filtering the circuit,

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

OK. So Vs(t) and Vn(t) are voltage generators with one end grounded.
Presumably, Vs(t) can have a very high SNR.

Between 3 - 20.

Moreover, there are four
nodes, and L and L! form an inductive voltage divider. Why is noise a
problem? Are the inductances very small?

Small compared to what?

In this case L = ~ 4 L1

Why not simply short out Vn(t)?

Supposing that isn't possible?

to determine the unknown inductance L,

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

There is no need to differentiate. The ratio of the voltages across the
inductors is the ratio of the inductances.

Supposing the voltage across L1 is unknown or very expensive and/or
inaccurate?


Bret Cahill