Uncorrelated noise

The term uncorrelated noise refers to a noise source being uncorrelated to a signal or another noise source.^[1] White noise in particular, due to its randomness, is uncorrelated to any other signal and is also serially uncorrelated (i.e., later values of it have no correlation to earlier values). Thus, "uncorrelated noise" is sometimes imprecisely^{[citation needed]} used synonymously with "white noise". However, in general, noise sources can have any noise spectrum and may or may not be correlated with each other (in practice different noise sources are usually uncorrelated^[2]). This situation is sometimes described as "uncorrelated colored noise".^[3]

Uncorrelated noise in electronics

Electronic circuits may have many types of electronic noise.

If the noise sources are uncorrelated with each other, those noise sources add according to the sum of their power.^[2] Thus, when expressed as voltages or currents (${\displaystyle e_{1},\,e_{2},\,\cdots \,e_{n}}$), the square of the total noise (${\displaystyle e_{\text{total}}^{2}}$) is the sum of squares of the individual noise sources (${\displaystyle e_{1}^{2}+e_{2}^{2}+\cdots +e_{n}^{2}}$). In other words, the total noise voltage or current (${\displaystyle e_{\text{total}}}$) is the square root of that sum of squares:

$${\displaystyle e_{\text{total}}={\sqrt {e_{1}^{2}+e_{2}^{2}+\cdots +e_{n}^{2}}}\,.}$$

References

1. Kay, A. (2012). Operational Amplifier Noise: Techniques and Tips for Analyzing and Reducing Noise. Elsevier Science. p. 217. ISBN 978-0-08-094243-8. Retrieved 2024-04-08.
2. Sobering, Tim J. (1999). "Noise in Electronic Systems" (PDF). Archived (PDF) from the original on 2023-05-20. Retrieved 2024-04-07.
3. Luo, Jun; Liu, Gang; Huang, Zongming; Law, S.S. (2019). "Mode shape identification based on Gabor transform and singular value decomposition under uncorrelated colored noise excitation". Mechanical Systems and Signal Processing. 128: 446–462. Bibcode:2019MSSP..128..446L. doi:10.1016/j.ymssp.2019.04.002.