Summing noise

1. Dec 14, 2008

evidenso

hello
well I have 2 vectors in matlab each representing a signal+shot noise. I have to add them. Can anyone tell me what the signal noise ratio will be when they are added?

thanks MB

2. Dec 15, 2008

Staff: Mentor

If this is homework/coursework, I can move the thread to the Homework Help forums.

What are your thoughts on how to add signals and noise? What constraints can you place on the noise in these two signals? For example, is the noise correlated in any way between the two signals? Why would that be important?

3. Dec 15, 2008

evidenso

No home assignment. I have to use it for investigating whether Raman SSRS degrades SNR :) but thats a whole other story for physcisians

I have to know if adding 2 noise sources gives more noise? lets say it is gaussian noise and I have 2 vectors with signal1 + noise1 and signal2+noise2

I recall it's something with 1/sqrt(2)(noise_1+noise_2) but I cant fint any material on the net.

4. Dec 15, 2008

D H

Staff Emeritus
That rule of thumb assumes a lot: Uncorrelated, unbiased, gaussian noise. berkeman already mentioned the issue of correlated noise. I'll add another: bias. If your measurements are consistently high (or low), taking a lot of measurements will not help address the measurement problem.

5. Dec 15, 2008

Staff: Mentor

I'm not an expert on noise, so I'll let others chime in with better answers. But I did google adding noise sources rms, and got some good hits. Here's one hit from that search, centered more on on vibration noise, but with mathematical treatment that is more generally applicable:

http://www.techmfg.com/techbkgd/techbkgd_1.html [Broken]

Last edited by a moderator: May 3, 2017
6. Dec 15, 2008

D H

Staff Emeritus
Dang. Modeling noise is one of the hats I wear. Unfortunately, I'm getting a lot of noise from my family about dinner.

Handling noise properly is not a simple topic. One can take graduate-level classes in which noise figures prominently. Some starters for google: Weiner filter, Kalman filter, recursive least squares filter, ...

7. Dec 15, 2008

davidrit

summed noise = sqrt(noise1^2 + noise^2) if uncorrelated and Gaussian The approximation given can yield a total noise lower than each individual component, I wish it were that easy to get rid of noise.

What's the relative size of the two noise components? Since they add in quadrature the larger one often strongly dominates.

8. Dec 15, 2008

Proton Soup

i can't give you a satisfactory answer because it's been too many years since i worked with it, but i think the noise distribution on your signal may actually be non-gaussian. i'd suggest you either try doing some monte carlo simulations to convince yourself of your intuition, or look up some control theory on gaussian sums. looking up your question on google seems to show there's a difference here depending on whether what you're looking at is actually a mixture or a sum.

9. Dec 16, 2008