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

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.

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

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.

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

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

S1 =3D signal 1

S2 =3D signal 2

S1/S2 =3D desired output which would be a const. dc without noise.

N =3D noise

(S1 + N)/(S2 - N) =3D actual output.

Noise is amplified in output.

c =3D 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

the

nal

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.

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

g the

ignal

g the

ignal

It may very well be something like that.

What's the difference between noise and interference?

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

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

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.

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".

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.

ee

ing the

signal

be

er

"> 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

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.

Couldn't noise share a frequency band as well?

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

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'.