Rectification Quotient Sync Filter

[Bret Cahill]

Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed. The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.


Bret Cahill


"Fun is the father of invention."

-- Bret Cahill

 

[John Larkin]

On Wed, 5 Aug 2009 11:21:46 -0700 (PDT), Bret Cahill
<BretCahill@peoplepc.com> wrote:

Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed. The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.


Bret Cahill


"Fun is the father of invention."

-- Bret Cahill

Loonier and loonier. There's long-established mathematics that you
seem to know nothing about. You may as well try to violate
conservation of energy.

John

 

[Ace0f_5pades]

On Aug 6, 11:15 am, John Larkin
<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:

On Wed, 5 Aug 2009 11:21:46 -0700 (PDT), Bret Cahill



BretCah...@peoplepc.com> wrote:
Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed.  The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.

Bret Cahill

"Fun is the father of invention."

-- Bret Cahill

Loonier and loonier. There's long-established mathematics that you
seem to know nothing about. You may as well try to violate
conservation of energy.

John

oh? so what about friction?

 

[Bret Cahill]

Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed.  The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.

Bret Cahill

"Fun is the father of invention."

-- Bret Cahill

Loonier and loonier. There's long-established mathematics that you
seem to know nothing about.

Someone will need to show it.

You may as well try to violate
conservation of energy.

I just finished trying to do that at the local pool.

Assume:

The pool temp is 93 degrees F.

The delta T through the skin is 3 F.

The Reynolds number for a swimmer at 2.6 ft/sec is 10^6.

The HX coefficient of a swimmer in water is 500 watt/m^2 - C.

Swimming 2.6 ft/sec requires 200 watts mechanical energy.

If human metabolism is 30% efficient what is my surface area?


Bret Cahill

 

[Bret Cahill]

Rectification doesn't do much to solve the unbounded quotient
problem. Instead of +/- infinity you get + infinity.

An alert math person brought this to my attention.


Bret Cahill


"Be alert. America needs more lerts."

Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed.  The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.

Bret Cahill

"Fun is the father of invention."

-- Bret Cahill

 

[John Larkin]

On Wed, 5 Aug 2009 20:26:16 -0700 (PDT), Bret Cahill
<BretCahill@aol.com> wrote:

Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed.  The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.

Bret Cahill

"Fun is the father of invention."

-- Bret Cahill

Loonier and loonier. There's long-established mathematics that you
seem to know nothing about.

Someone will need to show it.

Start here:

http://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication

John

 

[Bret Cahill]

Rectify both the signal and the ref along with their noise components
_then_ divide.

Since there are no humps from multiplying two in sync signals as with
lock in, only the noise needs to be smoothed.  The time constant could
be lower, much much lower at low noise levels.

At high noise levels the time constant would increase but it would it
would always remain below lock in.

Rectification quotient sync is superior to lock in for every
application.

Bret Cahill

"Fun is the father of invention."

-- Bret Cahill

Loonier and loonier. There's long-established mathematics that you
seem to know nothing about.

Someone will need to show it.

Start here:

http://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero. After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.


Bret Cahill

 

[Benj]

On Aug 7, 10:51 am, Bret Cahill <BretCah...@peoplepc.com> wrote:

Start here:

http://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication

It doesn't seem too long but I don't think I need it now.

You obviously don't need to know anything to shoot off your mouth!
I recommend staying that way as you'll use less Prozac.

 

[Jasen Betts]

On 2009-08-07, Bret Cahill <BretCahill@peoplepc.com> wrote:

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero. After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.

sounds like an envelope detector.

that'll not have the narrow-band response of the lock-in,

 

[John Larkin]

On Sat, 8 Aug 2009 15:24:59 -0700 (PDT), Bret Cahill
<BretCahill@peoplepc.com> wrote:

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.

sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync. The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True. My problem isn't noise but time. I only get 6 cycles max.


Bret Cahill

You should get out more.

http://en.wikipedia.org/wiki/Matched_filter

John

 

[Bret Cahill]

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.

sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync. The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True. My problem isn't noise but time. I only get 6 cycles max.


Bret Cahill

 

[Bret Cahill]

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.

sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync.  The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True.  My problem isn't noise but time.  I only get 6 cycles max.

Bret Cahill

You should get out more.

http://en.wikipedia.org/wiki/Matched_filter

Someone else also suggested matched filters a few weeks ago. That
may be the way to go.

Plan "A" is to get away with as few sensors and wires as possible.

Still it's good to know there is a plan "B" or "C."


Bret Cahill

 

[John Larkin]

On Sun, 9 Aug 2009 16:30:02 -0700 (PDT), Bret Cahill
<BretCahill@peoplepc.com> wrote:

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.
sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync.  The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True.  

My problem isn't too much noise but too little time.  I only get 6
cycles max.

Some EE or electronics poster, maybe from here, posted on
sci.mech.engr that he had invented a heat sink that relied on the high
heat transfer due to condensation and evaporation of a fluid in a
tube. Someone told him that heat pipes had been on the market and
studied in depth for decades.

He was delighted.

Now we can easily guess several things:

1. dividing 2 in sync signals is done all the time.

I've designed and studied a lot of electronics, and I've never seen it
done. Got any references?

2. the time to smooth a rectified AC to a DC output is frequently an
issue.

We use things called "filters", about which there's a lot of history
and math.

3. someone decades ago probably tried to lower the time constant in
the situation above by using a low time constant prefilter to keep the
denominator a small amount above zero and then letting the division of
the two signals do most of the heavy lifting as far as smoothing the
quotient to DC in a short time.

Doubt it.

John

 

[Bret Cahill]

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.
sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync.  The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True.  

My problem isn't too much noise but too little time.  I only get 6
cycles max.

Some EE or electronics poster, maybe from here, posted on
sci.mech.engr that he had invented a heat sink that relied on the high
heat transfer due to condensation and evaporation of a fluid in a
tube. Someone told him that heat pipes had been on the market and
studied in depth for decades.

He was delighted.

Now we can easily guess several things:

1. dividing 2 in sync signals is done all the time.

2. the time to smooth a rectified AC to a DC output is frequently an
issue.

3. someone decades ago probably tried to lower the time constant in
the situation above by using a low time constant prefilter to keep the
denominator a small amount above zero and then letting the division of
the two signals do most of the heavy lifting as far as smoothing the
quotient to DC in a short time.


Bret Cahill



Bret Cahill







Bret Cahill

 

[John Larkin]

On Sun, 9 Aug 2009 18:29:30 -0700 (PDT), Bret Cahill
<BretCahill@peoplepc.com> wrote:

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.
sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync.  The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True.  

My problem isn't too much noise but too little time.  I only get 6
cycles max.

Some EE or electronics poster, maybe from here, posted on
sci.mech.engr that he had invented a heat sink that relied on the high
heat transfer due to condensation and evaporation of a fluid in a
tube.  Someone told him that heat pipes had been on the market and
studied in depth for decades.

He was delighted.

Now we can easily guess several things:

1.  dividing 2 in sync signals is done all the time.

I've designed and studied a lot of electronics, and I've never seen it
done. Got any references?

Now that you mention it, there was never anything similar to my
particular application/solution, at least not in that field. Judging
from that alone maybe it shouldn't be too astounding that there was
never any motivation for the circuit before now.

2.  the time to smooth a rectified AC to a DC output is frequently an
issue.

We use things called "filters", about which there's a lot of history
and math.

But nothing on quotients of 2 signals . . .

3.  someone decades ago probably tried to lower the time constant in
the situation above by using a low time constant prefilter to keep the
denominator a small amount above zero and then letting the division of
the two signals do most of the heavy lifting as far as smoothing the
quotient to DC in a short time.

Doubt it.

They have all these circuits as complicated as the Palo Verde nuke
plant so it is hard to believe that something as simple as this
situation, a DC output that consists of the quotient of two AC
signals, hasn't appeared before now.

Oh, division of analog signals has been done for 60 years at least.
But not in the way you suggest.

John

 

[Bret Cahill]

It doesn't seem too long but I don't think I need it now.

Basic strategies to keep time constant(s) down might be interesting.

Dividing low noise AC signals will work if they are first either
rectified or multiplied by a ref and then smoothed just enough to keep
the denominator a certain distance that increases with noise above
zero.  After that one is divied by the other so only the noise needs
to be smoothed, not the humps from the wave forms.

The two low time coinstants would be much lower than the one big one
if the waves are smoothed in one step after rectification.

This has probably been done before and there might even be a name for
it.
sounds like an envelope detector.

There's no modulation, just one signal being divided by another signal
that happens to be in sync.  The amplitudes only change ~ 1% over 4 -
6 cycles.

Both signals could be rectified and smoothed and then divided for the
output but the output needs to be 99.5% smooth in just 4 - 6 cycles so
smoothing each signal all at once _before_ the division probably won't
work.

To save time both signals could be smoothed just enough before
division to keep the denominator above zero.

After that it will be possible divide the slightly modified signals
for a relatively smooth output.

If a second smoothing is necessary both time constants should be less
than smoothing all at once before the division.

Noise isn't directly an issue because the noise is only 10% of the
signal and already has a short enough time const..

that'll not have the narrow-band response of the lock-in,

True.  

My problem isn't too much noise but too little time.  I only get 6
cycles max.

Some EE or electronics poster, maybe from here, posted on
sci.mech.engr that he had invented a heat sink that relied on the high
heat transfer due to condensation and evaporation of a fluid in a
tube.  Someone told him that heat pipes had been on the market and
studied in depth for decades.

He was delighted.

Now we can easily guess several things:

1.  dividing 2 in sync signals is done all the time.

I've designed and studied a lot of electronics, and I've never seen it
done. Got any references?

Now that you mention it, there was never anything similar to my
particular application/solution, at least not in that field. Judging
from that alone maybe it shouldn't be too astounding that there was
never any motivation for the circuit before now.

2.  the time to smooth a rectified AC to a DC output is frequently an
issue.

We use things called "filters", about which there's a lot of history
and math.

But nothing on quotients of 2 signals . . .

3.  someone decades ago probably tried to lower the time constant in
the situation above by using a low time constant prefilter to keep the
denominator a small amount above zero and then letting the division of
the two signals do most of the heavy lifting as far as smoothing the
quotient to DC in a short time.

Doubt it.

They have all these circuits as complicated as the Palo Verde nuke
plant so it is hard to believe that something as simple as this
situation, a DC output that consists of the quotient of two AC
signals, hasn't appeared before now.

I'm not very interested in patenting a "filter" or time const.
lowering strategy that only has one application.


Bret Cahill

 

[whit3rd]

On Aug 9, 7:30 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

Now we can easily guess several things:

1.  dividing 2 in sync signals is done all the time.

No, usually one samples the signals, say X and Y,
and does a least-squares fit to determine
Y= aX + b
and on finding b approximately equal to zero, one has
a good value for the ratio, 'a'.
Division isn't a necessary step at all. Accumulating
(in this case, integrating) values like X, Y, X**2, X*Y,
and doing some arithmetic ON THE SUMS.

2.  the time to smooth a rectified AC to a DC output is frequently an
issue.

It's less than 'an issue', it's a failure to define the terms. AC
measurement by making a DC conversion only works if you have
some kind of average in mind (AC is a vector, DC is a scalar; they
aren't ever 'equivalent'). It's not clear that the best 'm' value
in the linear equation is related to any averaging after division.

3.  someone decades ago probably tried to lower the time constant in
the situation above by using a low time constant prefilter to keep the
denominator a small amount above zero and then letting the division of
the two signals do most of the heavy lifting as far as smoothing the
quotient to DC in a short time.

Collect the data, do a least-squares fit, extract 'm' value. There's
no particular need for any 'time constant' or prefilter, no concern
with denominators.

 

[Androcles]

"whit3rd" <whit3rd@gmail.com> wrote in message
news:7c18a628-32c9-4b7a-baeb-4d33a4301cf7@j9g2000vbp.googlegroups.com...
On Aug 9, 7:30 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

Now we can easily guess several things:

1. dividing 2 in sync signals is done all the time.

No, usually one samples the signals, say X and Y,
and does a least-squares fit to determine
Y= aX + b

===================================
If Y = a.sin(b.X+c) can you still do a least-squares fit to the curve?








and on finding b approximately equal to zero, one has
a good value for the ratio, 'a'.
Division isn't a necessary step at all. Accumulating
(in this case, integrating) values like X, Y, X**2, X*Y,
and doing some arithmetic ON THE SUMS.

2. the time to smooth a rectified AC to a DC output is frequently an
issue.

It's less than 'an issue', it's a failure to define the terms. AC
measurement by making a DC conversion only works if you have
some kind of average in mind (AC is a vector, DC is a scalar;

============================================
You have that back arse-wards, boy.

 

[Androcles]

"whit3rd" <whit3rd@gmail.com> wrote in message
news:fe2de150-90c7-4e96-8457-8d9095c40023@o13g2000vbl.googlegroups.com...
On Aug 10, 7:19 am, "Androcles" <Headmas...@Hogwarts.physics_i> wrote:

"whit3rd" <whit...@gmail.com> wrote in message
... one samples the signals, say X and Y,
and does a least-squares fit to determine
Y= aX + b

If Y = a.sin(b.X+c) can you still do a least-squares fit to the curve?

Yes, of course, but that isn't a line-fit, and simple linear least-
squares
formulae for a line are built into calculators. Nonlinear fit with
three variable parameters (a, b, c) is usually done by computer
search followed by iterative improvements.
============================================
Who uses a calculator?

=============================================
We know the temperature
============================================
What does that have to do with DC being a vector?

 

[whit3rd]

On Aug 10, 7:19 am, "Androcles" <Headmas...@Hogwarts.physics_i> wrote:

"whit3rd" <whit...@gmail.com> wrote in message
... one samples the signals, say X and Y,
and does a least-squares fit to determine
 Y= aX + b

If Y = a.sin(b.X+c) can you still do a least-squares fit to the curve?

Yes, of course, but that isn't a line-fit, and simple linear least-
squares
formulae for a line are built into calculators. Nonlinear fit with
three variable parameters (a, b, c) is usually done by computer
search followed by iterative improvements.

We know the temperature and composition of the Sun because of
multiparameter fits to sunlight's spectrum. Helium was
discovered by folk who found that improving the fit required a new
(hitherto unknown) element.