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If the noise is orders of magnitude higher than the signal, tossingInstead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
Only if the noise occupies a higher frequency band
than the signal.
If the signal is being divided by an in phase ref, then it's _already_
DC, at least everywhere the ref isn't zero.
The only AC is due to the noise.
If that's the case, your capacitor
on its own will filter out the noise, and you don't
need the lock-in arrangement at all.
Exactly!
The question is, does _anyone_ need a lock in when a quotient sync
filter is simpler and faster?
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
Only if the noise occupies a higher frequency band
than the signal.
If the signal is being divided by an in phase ref, then it's _already_
DC, at least everywhere the ref isn't zero.
The only AC is due to the noise.
If that's the case, your capacitor
on its own will filter out the noise, and you don't
need the lock-in arrangement at all.
Exactly!
The question is, does _anyone_ need a lock in when a quotient sync
filter is simpler and faster?
If the noise is orders of magnitude higher than the signal, tossing
20% to 50% of the signal just doesn't seem like a big advantage.
If the signal is several times larger than the noise and needs to be
increased to 500 times larger, then the time saved can be critical.
Bret Cahill
Hey Bret,A lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt, the
output is sin^2(wt) which is always positive. Regardless of the
particular shape it can always be smoothed to a DC output proportional
to the signal -- with enough time.
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
A much greater advantage is when the noise drops, you aren't forced to
waste a lot of time smoothing a squared signal to DC.
It's already there.
Quotient sync filtering is better than lock in in every respect.
Bret Cahill
This isn't some epidemiology study on the public health effects ofA lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt, the
output is sin^2(wt) which is always positive. Regardless of the
particular shape it can always be smoothed to a DC output proportional
to the signal -- with enough time.
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
A much greater advantage is when the noise drops, you aren't forced to
waste a lot of time smoothing a squared signal to DC.
It's already there.
Quotient sync filtering is better than lock in in every respect.
Bret Cahill
Hey Bret,
are you talking from a theoretical perspective, or actually results?
And?Isn't it the case that even the timing signal has transition noise
between on and off.
Again?In which perhaps double the processing power
applied to considering the union of split timing signal (by 2)?
He is talking from personal delusions. He has never done the tests.On Aug 2, 1:31 am, Bret Cahill <BretCah...@peoplepc.com> wrote:
A lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt, the
output is sin^2(wt) which is always positive. Regardless of the
particular shape it can always be smoothed to a DC output proportional
to the signal -- with enough time.
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
A much greater advantage is when the noise drops, you aren't forced to
waste a lot of time smoothing a squared signal to DC.
It's already there.
Quotient sync filtering is better than lock in in every respect.
Bret Cahill
Hey Bret,
are you talking from a theoretical perspective, or actually results?
Isn't it the case that even the timing signal has transition noise
between on and off. In which perhaps double the processing power
applied to considering the union of split timing signal (by 2)?
So you have not done the experiments or the theory.A lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt, the
output is sin^2(wt) which is always positive. Regardless of the
particular shape it can always be smoothed to a DC output proportional
to the signal -- with enough time.
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
A much greater advantage is when the noise drops, you aren't forced to
waste a lot of time smoothing a squared signal to DC.
It's already there.
Quotient sync filtering is better than lock in in every respect.
Bret Cahill
Hey Bret,
are you talking from a theoretical perspective, or actually results?
This isn't some epidemiology study on the public health effects of
eating broccoli.
You means you have not done any study on this.This can be determined right here right now by first principles.
Yes?Isn't it the case that even the timing signal has transition noise
between on and off.
And?
In which perhaps double the processing power
applied to considering the union of split timing signal (by 2)?
Again?
Bret Cahill
"The superman is the lightening out of the dark cloud man."
-- Nietzsche
So why do your signal to noise conversion instead of doing it correctly?Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
Only if the noise occupies a higher frequency band
than the signal.
If the signal is being divided by an in phase ref, then it's _already_
DC, at least everywhere the ref isn't zero.
The only AC is due to the noise.
If that's the case, your capacitor
on its own will filter out the noise, and you don't
need the lock-in arrangement at all.
Exactly!
The question is, does _anyone_ need a lock in when a quotient sync
filter is simpler and faster?
If the noise is orders of magnitude higher than the signal, tossing
20% to 50% of the signal just doesn't seem like a big advantage.
If the signal is several times larger than the noise and needs to be
increased to 500 times larger, then the time saved can be critical.
Bret Cahill
Multipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
Only in situations so limited they aren't worth considering.
have been wanting to ignroe them.A lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
OK, how much money is at stake? I can put the original idea on the
back burner for awhile if necessary.
Well, you should at least try to follow the laws of physics. You
Yes, just hope and pray instead of actually working.Previously I just wanted to plug something into a net book and then
call it a day.
Bret Cahill
Only in situations so limited they aren't worth considering.Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
Only if the noise occupies a higher frequency band
than the signal.
If the signal is being divided by an in phase ref, then it's _already_
DC, at least everywhere the ref isn't zero.
The only AC is due to the noise.
If that's the case, your capacitor
on its own will filter out the noise, and you don't
need the lock-in arrangement at all.
Exactly!
The question is, does _anyone_ need a lock in when a quotient sync
filter is simpler and faster?
If the noise is orders of magnitude higher than the signal, tossing
20% to 50% of the signal just doesn't seem like a big advantage.
If the signal is several times larger than the noise and needs to be
increased to 500 times larger, then the time saved can be critical.
Bret Cahill
Multipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
OK, how much money is at stake? I can put the original idea on theA lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
Agreed, except in most circumstances the minimumMultipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
A lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
This is absolutely true but the traditional lockinOn Sun, 02 Aug 2009 18:21:37 -0700, John Larkin
jjlarkin@highNOTlandTHIStechnologyPART.com
wrote:
Multipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
A lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
Agreed, except in most circumstances the minimum
requirement is to send the input signal to *two*
separate multipliers, and multiply by the
reference in sine and cosine phases, then use the
recovered DC values to compute magnitude.
Otherwise, with a single reference multiply, you
get huge errors due to signal phase changes...
including getting no output at all if the signal
has undergone a 90 degree phase shift.
Best regards,
Bob Masta
DAQARTA v4.51
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
FREE Signal Generator
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Limiting the fraction of the time you look at a signal means aMultipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
A lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
Agreed, except in most circumstances the minimum
requirement is to send the input signal to *two*
separate multipliers, and multiply by the
reference in sine and cosine phases, then use the
recovered DC values to compute magnitude.
Otherwise, with a single reference multiply, you
get huge errors due to signal phase changes...
including getting no output at all if the signal
has undergone a 90 degree phase shift.
Quotient sync requires knowing when the reference is near zero.
Other than that the phase angle between the signal and the ref are
treated in a manner equivalent to any conventional lock in.
That drawback seems minor even in the case of low SNR as the sampling
angle can be adjusted to an optimum. A larger sample angle extracts
more information from the signal but increases the noise monitored
when the denominator is near zero. A smaller sample angle decreases
the noise when the ref is near zero but it also decreases the signal
sample.
Well, no, the laws of physics do not depend on the SNR.The big advantage with quotient sync is in the case of high SNR where
the amplitude of the signal needs to be known to a high degree of
precision.
You really have done no signal processing or analysis.Only the noise needs to be smoothed so the "aquisition" time is much
shorther.
So if you don't know the SNR or if the SNR varies wildly, quotient
sync could save a lot of time out in the field.
Except, of course, that it is a silly way to do anything.
Bret Cahill
Quotient sync requires knowing when the reference is near zero.Multipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
A lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
Agreed, except in most circumstances the minimum
requirement is to send the input signal to *two*
separate multipliers, and multiply by the
reference in sine and cosine phases, then use the
recovered DC values to compute magnitude.
Otherwise, with a single reference multiply, you
get huge errors due to signal phase changes...
including getting no output at all if the signal
has undergone a 90 degree phase shift.
So? whats that got to do with the price of fish?A lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt, the
output is sin^2(wt) which is always positive. Regardless of the
particular shape it can always be smoothed to a DC output proportional
to the signal -- with enough time.
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
A much greater advantage is when the noise drops, you aren't forced to
waste a lot of time smoothing a squared signal to DC.
It's already there.
Quotient sync filtering is better than lock in in every respect.
Bret Cahill
Hey Bret,
are you talking from a theoretical perspective, or actually results?
This isn't some epidemiology study on the public health effects of
eating broccoli.
I agree in principle, but saying a thing isn't the thing.This can be determined right here right now by first principles.
Well, for the lim x-->1 f(x) = (xx-1)/(x-1) .... that limit is 2...Isn't it the case that even the timing signal has transition noise
between on and off.
And?
all) separated by transition.In which perhaps double the processing power
applied to considering the union of split timing signal (by 2)?
Again?
was thinking (applications of two times rising-edges & falling-edge is
if you think so, but that aint it to me. The spark is the lightning.Bret Cahill
"The superman is the lightening out of the dark cloud man."
-- Nietzsche
Mathematically, the original multiply/integrate action of a lock inA lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt,
....
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
Near the signal zero crossings, you'd be applying an enormous
amount of gain to what's left, namely the noise and offset.
The solution would be to only sample outside a certain +/- angle when
both the signal and ref are zero
A very minor loss in almost all applications.A lock in amplifier multiplies an AC signal + noise by a synchronous
reference signal. If the signal is sinwt and the ref is sinwt,
...
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
Near the signal zero crossings, you'd be applying an enormous
amount of gain to what's left, namely the noise and offset.
The solution would be to only sample outside a certain +/- angle when
both the signal and ref are zero
Mathematically, the original multiply/integrate action of a lock in
amplifier is an inner product, and produces the full value of the
in-frequency signal with zero out-of-band noise. The action
of a 'divide' does produce high noise sensitivity in out-of-band
regions, and the proposed 'only outside a certain angle' will
reduce noise BUT ALSO reduce signal.
The "aquisition time" of a conventional lock in is much too long inThe phase-locked amplifier with reference multiplication is better
both on signal recovery (gain) and noise rejection.
Apparently they aren't too concerned about losing some signal info.Other phase-locked amplifiers use a square-wave reference,
I may get back into signal recovery in a few months if there's anyand
capture a few harmonics of the fundamental; those (so-called boxcar
averagers) are using a reference that goes from +1 to -1, so the
'multiply' versus 'divide' is a distinction without a difference,
and they DO work, just not quite the same as sinewave
multiplying units.
There's a real way to improve signal * reference type phase-locked
amps, and it is to add a statistical weight function, i.e.
signal * reference * W(phase, time, temperature)
where W is a positive definite function that is proportional to
the inverse of the expected squared amplitude of the signal
measurement error (1/sigma-squared). That weight function
would track any conditions that reduce the expected signal measurement
error (and would, in the case of the 'divide' algorithm, pretty much
undo the division, and for completely sound mathematical
reasons).
If you were looking at starlight, the W function would turn your
experiment off during daylight hours when lots of scattered
sunlight was dominant. It's what an experimenter would
do 'by hand' in that simple case.
Or, it's important to reject one phase, the 90-degree-from-referenceOther phase-locked amplifiers use a square-wave reference,
Apparently they aren't too concerned about losing some signal info.
The "aquisition time" of a conventional lock in is much too long in
many situations.
Huh? All the lock-ins I have seen use the fullA lot of conventional lock in applications only sample part of _one_
cycle _anyway_.
two different aspects of lock-in amps.The phase-locked amplifier with reference multiplication is better
both on signal recovery (gain) and noise rejection.
The "aquisition time" of a conventional lock in is much too long in
many situations.
I'm beginning to wonder if maybe you are confusing
Yup, Except for some signals that last only for a short time comparedOn Sun, 2 Aug 2009 06:59:32 -0700 (PDT), Bret Cahill
BretCah...@aol.com> wrote:
Instead of multiplying it would be better to _divide_ the noisy AC
signal by the ref.
One advantage over lock in is a simple capacitor in parallel with the
output shorts out the AC component which is the noise.
Only if the noise occupies a higher frequency band
than the signal.
If the signal is being divided by an in phase ref, then it's _already_
DC, at least everywhere the ref isn't zero.
The only AC is due to the noise.
If that's the case, your capacitor
on its own will filter out the noise, and you don't
need the lock-in arrangement at all.
Exactly!
The question is, does _anyone_ need a lock in when a quotient sync
filter is simpler and faster?
If the noise is orders of magnitude higher than the signal, tossing
20% to 50% of the signal just doesn't seem like a big advantage.
If the signal is several times larger than the noise and needs to be
increased to 500 times larger, then the time saved can be critical.
Bret Cahill
Multipling the signal+noise by a reference sine wave, and averaging
the result, is mathematically equivalent to doing the exactly-best
complex discrete Fourier transform and taking the in-phase component
as the result. You can't do better than that.
A lot of very smart people have thought about this for a very long
time, in situations where a small increase in s/n ratio is worth
gigabucks.
John- Hide quoted text -
- Show quoted text -
We may be using one word for two different things.A lot of conventional lock in applications only sample part of _one_
cycle _anyway_.
Huh? All the lock-ins I have seen use the full
cycle... that's the referene frequency. The time
constant controls the number of cycles used.
The phase-locked amplifier with reference multiplication is better
both on signal recovery (gain) and noise rejection.
The "aquisition time" of a conventional lock in is much too long in
many situations.
I'm beginning to wonder if maybe you are confusing
two different aspects of lock-in amps.
Consider a hypothetical problem:"Acquisition time" includes the time for the
phase-locked loop in the lock-in to lock to the
signal. The time constant controls the S/N
improvement.
PLL lock time is totally unneeded if you already
have the reference signal in sin/cos phases.
I don't know the current situation, but for years
lock-in makers seemed wedded to the idea of only
using the PLL to generate the reference. Even
when they provided a voltage-controlled reference,
it was a simple oscillator that fed into the PLL
to get sin/cos, instead of just controlling the
PLL VCO directly. Duh!
So, if you are dismayed by long lock-in
acquisition times from a lock-in simulator, maybe
things aren't as bad as you think. Maybe they are
just dutifully including PLL lock time in the
simulation.
DAQARTA v4.51
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
FREE Signal Generator
Science with your sound card!
It sounds like you are looking for a single constant valueIn reality there is noise and dividing AC signals won't work because
the denominator will approach zero with noise in the numerator. The
quotient then becomes undefined, +/- infinity. In fact, the quotient
would become undefined at 0 / 0 even without any noise.
Instead of sampling away from the zero intersections, as initially
suggested as a solution, rectify both signals along with their noise
components _then_ divide.