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

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Discussion Overview

The discussion revolves around the addition of two vectors in MATLAB, each representing a signal combined with shot noise. Participants explore the implications for signal-to-noise ratio (SNR) when these signals are combined, particularly in the context of Gaussian noise and its characteristics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • MB inquires about the SNR when adding two vectors of signal plus noise and expresses a need for clarity on the outcome.
  • Some participants question the correlation between the noise in the two signals and its importance in determining the resultant noise.
  • One participant recalls a formula involving the square root of the sum of the squares of the noise components, noting that it assumes uncorrelated, unbiased, Gaussian noise.
  • Another participant mentions that bias in measurements can affect the noise characteristics and suggests that simply taking more measurements may not resolve the issue.
  • A participant points out that the relative sizes of the noise components matter, as they add in quadrature, with the larger component often dominating the total noise.
  • There are suggestions to consider Monte Carlo simulations or control theory to better understand the noise distribution, which may not be purely Gaussian.
  • One participant provides a link to a resource discussing the addition of noise sources, indicating that the topic is complex and may require deeper investigation.
  • Another participant confirms that the sum of two uncorrelated Gaussian variables remains Gaussian, referencing a Wikipedia article for further reading.

Areas of Agreement / Disagreement

Participants express varying degrees of uncertainty regarding the characteristics of the noise when adding the two signals. There is no consensus on the implications of noise correlation, the validity of the Gaussian assumption, or the best methods to analyze the situation.

Contextual Notes

Participants highlight the complexity of modeling noise, indicating that assumptions about noise characteristics (e.g., correlation, bias) significantly influence the analysis. The discussion also reflects a lack of definitive resources or established methods for the specific scenario presented by MB.

Who May Find This Useful

This discussion may be of interest to those involved in signal processing, noise analysis, or related fields in physics and engineering, particularly in contexts where understanding the interaction of signals and noise is crucial.

evidenso
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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
 
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evidenso said:
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?
 
berkeman said:
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.
 
evidenso said:
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.
 
evidenso said:
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
 
Last edited by a moderator:
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, ...
 
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.
 
evidenso said:
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.
 

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