Adding Signal and Shot Noise in MATLAB - MB's Question

[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

 

[berkeman]

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

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?

 

[evidenso]

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?

No home assignment. I have to use it for investigating whether Raman SSRS degrades SNR :) but that's a whole other story for physicsians

I have to know if adding 2 noise sources gives more noise? let's 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 can't fint any material on the net.

 

[D H]

I recall it's something with 1/sqrt(2)(noise_1+noise_2) but I can't fint any material on the net.

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.

 

[berkeman]

No home assignment. I have to use it for investigating whether Raman SSRS degrades SNR :) but that's a whole other story for physicsians

I have to know if adding 2 noise sources gives more noise? let's 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 can't fint any material on the net.

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

 

[D H]

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, ...

 

[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.

 

[Proton Soup]

No home assignment. I have to use it for investigating whether Raman SSRS degrades SNR :) but that's a whole other story for physicsians

I have to know if adding 2 noise sources gives more noise? let's 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 can't fint any material on the net.

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.

 

[Proton Soup]

this was still bugging me so i finally looked it up. it is indeed gaussian if the two are uncorrelated.

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