B Does the Amplitude of White Noise Double When Two Samples are Added Together?

AI Thread Summary
When two samples of white noise with equal amplitude are added together, the resulting sample does not have double the amplitude; instead, the squared amplitudes add, leading to an increase in average power. The discussion also touches on pink noise, which behaves similarly under addition, maintaining its characteristics through Fourier transformation. Constants in the Fourier transformation, denoted as cf and cg, represent the contributions of each noise sample. The uncorrelated nature of the noise sources implies no fixed phase relation, supporting the conclusion that average powers, rather than amplitudes, sum. Overall, the addition of uncorrelated noise samples results in a more complex interaction than simply doubling the amplitude.
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Suppose you have two samples of white noise of equal amplitude. If you add them together ((sub)sample-by-(sub)sample that is), do you get one sample of white noise with twice the amplitude?

How about pink noise?
 
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Both white and pink noise are defined by their Fourier transform (see http://applet-magic.com/spectrum1.htm), which is linear.

Suppose you have two time functions of white noise, f(t) and g(t). The Fourier transform of αf(t)+βg(t) is αFf+βFg = αcf+βcg, which is the Fourier transform of another white noise. So αf(t)+βg(t) is white noise.

Likewise, if f(t) and g(t) are pink noise, the Fourier transform of αf(t)+βg(t) is αFf+βFg = αcf/ω+βcg/ω = (αcf+βcg)/ω, which is the Fourier transform of another pink noise. So αf(t)+βg(t) is pink noise.
 
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What does cf (and cg) mean? Is it a constant function? Is Ff (Fg) the Fourier spectrum?

My terminology may be faulty; I have enjoyed a scientific education, but I have never been particularly good at math...o_O
 
Sorry, I should have been more careful. If you look in the link I posted you will see that there are constants, c, in the Fourier transformation of white and pink noise. cf and cg are the constants associated with f and g. Ff and Fg are the Fourier transformations of f and g. (I could not get the LaTex script F to work immediately.)
 
If the noise sources are uncorrelated, they shouldn't have any fixed phase relation. I would expect the squared amplitudes to add, not the amplitudes.
 
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mfb said:
If the noise sources are uncorrelated, they shouldn't have any fixed phase relation. I would expect the squared amplitudes to add, not the amplitudes.
This is not a subject that I am expert at, but I think that means that the average powers sum.
 
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