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

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.

. . .

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))] =3D> L

? ? ?

Bret Cahill

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

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)?

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

Jerry

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

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

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))] =3D> L

Well?

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

What about,

"Various Categorizations of Reference Based Filters"

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.

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

Between 3 - 20.

Small compared to what?

In this case L =3D ~ 4 L1

Supposing that isn't possible?

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

Bret Cahill