Sum of 2 Noisy Signals Makes Perfect Lock In Reference for B

[Bret Cahill]

Obviously the same noise causing one signal to increase is causing the
other to decrease.

Is this common? It may be a situation where the lock in can be
eliminated altogether with a little algebra.


Bret Cahill

 

[whit3rd]

On Feb 3, 8:05 am, Bret Cahill <BretCah...@peoplepc.com> wrote:

Obviously the same noise causing one signal to increase is causing the
other to decrease.

False inference, there. The 'sum of two signals' has twice the signal
but the noise is uncorrelated, so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

 

[Bret Cahill]

Obviously the same noise causing one signal to increase is causing the
other to decrease.

False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals. That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better. The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.


Bret Cahill

 

[John Larkin]

On Wed, 3 Feb 2010 21:38:46 -0800 (PST), Bret Cahill
<BretCahill@peoplepc.com> wrote:

Obviously the same noise causing one signal to increase is causing the
other to decrease.

False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals. That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better. The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.


Bret Cahill

I have no idea what you're talking about, and I suspect you don't
either.

John

 

[Bret Cahill]

S1 = signal 1

S2 = signal 2

S1/S2 = desired output which would be a const. dc without noise.

N = noise

(S1 + N)/(S2 - N) = actual output.

Noise is amplified in output.

c = const.

S1 + c(S2) is proportional to and has same phase angle as noise free
S1 as well as noise free S2 but is completely impervious to noise and
therefore can be used as a reference for lock in amp.

The question is, is this situation common in lock in amplification?


Bret Cahill

Obviously the same noise causing one signal to increase is causing the
other to decrease.
False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals.  That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better.  The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.

Bret Cahill

 

[George Herold]

On Feb 4, 11:45 am, Bret Cahill <BretCah...@peoplepc.com> wrote:

S1 = signal 1

S2 = signal 2

S1/S2 = desired output which would be a const. dc without noise.

N = noise

(S1 + N)/(S2 - N) = actual output.

Noise is amplified in output.

c = const.

S1 + c(S2)  is proportional to and has same phase angle as noise free
S1 as well as noise free S2 but is completely impervious to noise and
therefore can be used as a reference for lock in amp.

The question is, is this situation common in lock in amplification?

Bret Cahill



Obviously the same noise causing one signal to increase is causing the
other to decrease.
False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals.  That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better.  The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.

Bret Cahill- Hide quoted text -

- Show quoted text -

Not at all common! It sounds like what you are calling noise is
really interference. (Pick-up) The interference is getting in with
inverted phase on each of you signals. Then when you sum them the
interference goes away.... Best bet is to clean up your sigals such
that less interference gets in... What's the frequcny spectrum of your
'noise' look like and how big is it?

George H.

 

[John Larkin]

On Thu, 4 Feb 2010 08:45:07 -0800 (PST), Bret Cahill
<BretCahill@peoplepc.com> wrote:

S1 = signal 1

S2 = signal 2

S1/S2 = desired output which would be a const. dc without noise.

N = noise

(S1 + N)/(S2 - N) = actual output.

Noise is amplified in output.

c = const.

S1 + c(S2) is proportional to and has same phase angle as noise free
S1 as well as noise free S2 but is completely impervious to noise and
therefore can be used as a reference for lock in amp.

If S1 + c(S2) is as you say, then the final value of S1/S2 = K, where
K is any constant you like. So the output of your signal processing
box is a DC voltage, and you save a lot of money by eliminating input
connectors.

John

 

[Bret Cahill]

S1 = signal 1

S2 = signal 2

S1/S2 = desired output which would be a const. dc without noise.

N = noise

(S1 + N)/(S2 - N) = actual output.

Noise is amplified in output.

c = const.

S1 + c(S2)  is proportional to and has same phase angle as noise free
S1 as well as noise free S2 but is completely impervious to noise and
therefore can be used as a reference for lock in amp.

The question is, is this situation common in lock in amplification?

Bret Cahill

Obviously the same noise causing one signal to increase is causing the
other to decrease.
False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals.  That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better.  The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.

Bret Cahill- Hide quoted text -

- Show quoted text -

Not at all common!  It sounds like what you are calling noise is
really interference. (Pick-up)  The interference is getting in with
inverted phase on each of you signals.  Then when you sum them the
interference goes away.... Best bet is to clean up your sigals such
that less interference gets in... What's the frequcny spectrum of your
'noise' look like and how big is it?

George H.- Hide quoted text -

- Show quoted text -

 

[Bret Cahill]

S1 = signal 1

S2 = signal 2

S1/S2 = desired output which would be a const. dc without noise.

N = noise

(S1 + N)/(S2 - N) = actual output.

Noise is amplified in output.

c = const.

S1 + c(S2)  is proportional to and has same phase angle as noise free
S1 as well as noise free S2 but is completely impervious to noise and
therefore can be used as a reference for lock in amp.

The question is, is this situation common in lock in amplification?

Bret Cahill

Obviously the same noise causing one signal to increase is causing the
other to decrease.
False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals.  That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better.  The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.

Bret Cahill- Hide quoted text -

- Show quoted text -

Not at all common!  It sounds like what you are calling noise is
really interference. (Pick-up)  

It may very well be something like that.

What's the difference between noise and interference?

The interference is getting in with
inverted phase on each of you signals.  

The noise / interference doesn't have any frequency, shape or phase
angle in common with the signal.

Then when you sum them the
interference goes away.... Best bet is to clean up your sigals such
that less interference gets in... What's the frequcny spectrum of your
'noise' look like and how big is it?

The noise is about the same as the signal frequency, 0.2 to 0.8 Hz and
anywhere from 3% to 20% the amplitude of the signal.

It may not be relevant but 5 SNR on a lock in simulator only takes
about four cycles to get the noise down to 0.5% -- good enough.


Bret Cahill

 

[whit3rd]

On Feb 4, 8:15 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

What's the difference between noise and interference?

Noise is uncorrelated with any of the observable quantities.
Interference is a second party talking while you're trying to listen
to
yourself. Noise, therefore, is associated with entropy and
isn't informative, whereas the 'second party' might be VERY
informative.

The noise / interference doesn't have any frequency, shape or phase
angle in common with the signal.

Shape and phase angle are clumsy descriptions, but presumably you
mean the 'interference' is uncorrelated with the signal ON AVERAGE.
That doesn't mean it doesn't share a frequency band and randomly
come into/out of "phase".

It may not be relevant but 5 SNR on a lock in simulator only takes
about four cycles to get the noise down to 0.5% -- good enough.

Simulators cannot deal with interference in any correct fashion; if it
isn't "true" random noise, of a known quantity, the simulator would
need full information on the source of interference or will get
nonsense
answers.

 

[George Herold]

On Feb 4, 11:15 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

S1 = signal 1

S2 = signal 2

S1/S2 = desired output which would be a const. dc without noise.

N = noise

(S1 + N)/(S2 - N) = actual output.

Noise is amplified in output.

c = const.

S1 + c(S2)  is proportional to and has same phase angle as noise free
S1 as well as noise free S2 but is completely impervious to noise and
therefore can be used as a reference for lock in amp.

The question is, is this situation common in lock in amplification?

Bret Cahill

Obviously the same noise causing one signal to increase is causing the
other to decrease.
False inference, there.  The 'sum of two signals' has twice the signal

Depends on the 2 signals.  That's generally not true.

but the noise is uncorrelated,

In this case the sum of the two signals has the exact same shape and
phase angle as each noise free signal.

There's a very small chance this may suggest some algebraic solution
where the noise can be somehow subtracted and lock in filtering can be
avoided altogether.

so the sum of the two noises is
expected to be sqrt(2) times the individual noise values.

The quotient of the two signals is the goal so any magnitude change
from filtering will cancel out.

You are getting better signal/noise ratio in the sum than in either
of the two input terms, that's to be expected.

It isn't merely better.  The noise cancels out _altogether_ in the
sum.

The sum, however, isn't what is desired.

The sum is only useful as a reference to clean up the two signals.

It would be surprising in no one went down this path before on a
similar situation.

Bret Cahill- Hide quoted text -

- Show quoted text -

Not at all common!  It sounds like what you are calling noise is
really interference. (Pick-up)  

It may very well be something like that.

What's the difference between noise and interference?

The interference is getting in with
inverted phase on each of you signals.  

The noise / interference doesn't have any frequency, shape or phase
angle in common with the signal.

Then when you sum them the
interference goes away.... Best bet is to clean up your sigals such
that less interference gets in... What's the frequcny spectrum of your
'noise' look like and how big is it?

The noise is about the same as the signal frequency, 0.2 to 0.8 Hz and
anywhere from 3% to 20% the amplitude of the signal.

It may not be relevant but 5 SNR on a lock in simulator only takes
about four cycles to get the noise down to 0.5% -- good enough.

Bret Cahill- Hide quoted text -

- Show quoted text -

"> What's the difference between noise and interference?"

Noise is kinda a loose term, and is often used to include
interference. From my point of view I think of noise as the
fundamental 'stuff' that you can't get rid of. Johnson noise of
resistors, shot noise in diodes, I might also include amplifier noise
(Which unless you are going to build your own amplifier is kinda
fundamental.... you can't get rid of it by shielding your circuit,
moving it to a 'quite' location.)

Interference is all the crap coming into your circuit from the
outside. (Hmm OK you can have interference from some other part of
the circuit too... Digital switching spikes.)

Fundamental noise is uncoorelated. If you are summing two signals the
fundamental noise in one branch is uncoorelated with the noise in the
other... the signals add linearly and the noise adds in quadrature and
you get the 'expected' square root of two improvement in SNR.

Interfernce tends to be coorelated. If electro-static 'crap' from the
room lights is getting into one section of your circuit.. it will get
into the other piece in a similar way. (Both go away when the lights
are turned off.) When you sum the two signals it is then possible
that the interference from one branch is inverted when compared to the
other branch... then the sum of the two signals would show a much
bigger increase in SNR than the factor of root two above.

Look at the spectrum of your signal. (FFT on a digital scope.) Are
there spikes at say the AC line frequency and it's harmonics? Stuff
out at 20kHz to 40 kHz?


"> The noise is about the same as the signal frequency, 0.2 to 0.8 Hz
and

anywhere from 3% to 20% the amplitude of the signal."

That's a very low frequency! There may be 1/f noise from your
amplifiers and other things. Is your signal DC coupled? You can get
all sorts of DC offsets from various thermal things... but I don't
have much experience with very low frequency noise.

George H.

 

[Bret Cahill]

What's the difference between noise and interference?

Noise is uncorrelated with any of the observable quantities.
Interference is a second party talking while you're trying to listen
to
yourself.   Noise, therefore, is associated with entropy and
isn't informative, whereas the 'second party' might be VERY
informative.

The noise / interference doesn't have any frequency, shape or phase
angle in common with the signal.

Shape and phase angle are clumsy descriptions, but presumably you
mean the 'interference' is uncorrelated with the signal ON AVERAGE.
That doesn't mean it doesn't share a frequency band and randomly
come into/out of "phase".

Couldn't noise share a frequency band as well?

It may not be relevant but 5 SNR on a lock in simulator only takes
about four cycles to get the noise down to 0.5% -- good enough.

Simulators cannot deal with interference in any correct fashion; if it
isn't "true" random noise, of a known quantity, the simulator would
need full information on the source of interference or will get
nonsense
answers.

Does that mean a lock in approach won't work on interference?

Even if it did work it might be silly to use lock in when another
faster solution is available.


Bret Cahill

 

[whit3rd]

On Feb 5, 8:45 am, Bret Cahill <BretCah...@peoplepc.com> wrote:

Simulators cannot deal with interference in any correct fashion; if it
isn't "true" random noise, of a known quantity, the simulator would
need full information on the source of interference or will get
nonsense answers.

Does that mean a lock in approach won't work on interference?

What does that question mean? Lock-in amplifiers have very narrow
effective bandwidth, and it's tracking bandwidth so it can conform to
a signal. It can also conform to 'interference', which, after all, IS
ALSO
a signal.

Neither a simulator, nor a denizen of newsgroups, can make a useful
statement about unspecified 'interference' and its effect on an
unspecified
gizmo that is intended to achieve 'lock-in'.