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

[entropy1]

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?

 

[FactChecker]

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 αF_f+βF_g = αc_f+βc_g, 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 αF_f+βF_g = αc_f/ω+βc_g/ω = (αc_f+βc_g)/ω, which is the Fourier transform of another pink noise. So αf(t)+βg(t) is pink noise.

 

[entropy1]

What does c_f (and c_g) mean? Is it a constant function? Is F_f (F_g) the Fourier spectrum?

My terminology may be faulty; I have enjoyed a scientific education, but I have never been particularly good at math...

 

[FactChecker]

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. c_f and c_g are the constants associated with f and g. F_f and F_g are the Fourier transformations of f and g. (I could not get the LaTex script F to work immediately.)

 

[mfb]

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.

 

[FactChecker]

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.