Squar root and noise

Rockazella

Not sure if this is more a question for the physics forum or here, but ill start here.

I've been doing some reading on signal to noise calculations for video applications. In the reading it says that when you drop a certain signal by 2, the noise portion of it will only drop by
sqroot(2).
Don't really unsderstand where the sqroot comes in. Can anybody clear this up for me?

Guybrush Threepwood

I guess it had to do with the fact that you use the RMS value of the noise, but if you could elaborate more on the question....

Tyger

It has to do with the fact that photons are Bosons.

The photons in the signal are coherent, the probability of absorbing one is propertional to the number in a particular state, whereas the noise is incoherent, so adding more doesn't increase the probabilty of absorbing others.

Rockazella

I guess it had to do with the fact that you use the RMS value of the noise, but if you could elaborate more on the question....

Elaboration...

I don't know how familiar you are with video signals, but this question arose from a tech article on interlaced vs. non interlaced video cameras. Most video cameras are still interlaced, but that is changing. Interlaced cameras take a snapshot and then throw away all the even horizontal lines of resolution. 1/60th of a second later it takes another snapshot and then throws away the odd lines. Then it will combine the two (odd and even) lines into one frame. Progressive cams take a snapshot every 30th of a second and just save the whole thing as 1 frame.

The article said that since the signal in the progressive camera is dropped by 2, the image tends to have more noise. This is because when you drop the signal by 2 the noise is only dropped by sqroot(2). Thus you have an overall noisier signal.

So how does RMS explain this?

arcnets

The only explanation I can think of is a very simple one.
Say you have a signal of 200 with a noise of 2.
Now if you split that, you get 2 signals of 100 with a noise of 1.
Now since the noise is uncorrelated, you got 4 cases with equal probability:
101 + 101 = 202
99 + 101 = 200
101 + 99 = 200
99 + 99 = 198.
So you get an RMS noise of
sqrt((2^2 + 0^2 + 0^2 + 2^2)/4) = sqrt(2)

Guybrush Threepwood

so I guess it like arcnets said.

I'll try some math here to get used with the symbol making.... so excuse the eventual errors....

SNR = 10*log10(signal power/noise power) = 10*log10(S/N)

but noise power N = &radic;(&sigma;^2) (...that means RMS value)
&sigma;^2 is the variance of noise

if the noise is dropped by 2 the variance is dropped by 2
so the new noise power N1 = &radic;((&sigma;^2)/2)
and the noise drops only by sqrt(2)

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