I asked this question about zero-mean noise on Physics Stack Exchange and got this answer:

Zero mean so that the noise does not present a net disturbance to the system. There's as much positive noise as negative, so they cancel out in the long run. If the mean were not zero, then the noise would appear as an additional dynamic. For example, if the quantity were a force with some random jitter to it, then if the jitter did not have zero mean, the noise would appear as an additional net force on average.

I can't understand the meaning of the answer. What is another example of zero-mean noise, with an explanation from this answer?


closed as unclear what you're asking by Leon Heller, PeterJ, nidhin, Daniel Grillo, Adam Haun Apr 27 '15 at 17:24

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  • 2
    \$\begingroup\$ I don't understand your question. If noise has an average value of zero (which it will have), where does that get you? What is the "thing" that you are trying to work out? \$\endgroup\$ – Andy aka Apr 25 '15 at 13:36
  • \$\begingroup\$ You asked a question about zero-mean noise on Physics SE (physics.stackexchange.com/q/178323/60662) - why are you asking US to clarify it? Wouldn't that answerer know more about what he told you? \$\endgroup\$ – Greg d'Eon Apr 25 '15 at 19:06
  • \$\begingroup\$ @Gregd'Eon , Because I want to know the answer from who have another point of view. \$\endgroup\$ – gmotree Apr 26 '15 at 5:51

Consider the difference between errors due to rounding and truncation.

round(x) = integer(x + 0.5);
trunc(x) = integer(x);

With rounding, 1.4 will be rounded down to 1, but 1.6 will be rounded up to 2. With truncation, both results will be 1.

So round(1.4) + round(1.6) will be 3, as it should be, but trunc(1.4) + trunc(1.6) = 2.

This only illustrates the difference, but long term statistics will bear out the same observation.

This shows that rounding errors are a form of zero mean noise, while truncation errors are not. The long term mean value of truncation errors is -0.5 units, not 0.

  • \$\begingroup\$ Thanks Sir,did you mean that the "zero mean" means residual error? \$\endgroup\$ – gmotree Apr 25 '15 at 13:41
  • \$\begingroup\$ I cannot understand your comment. \$\endgroup\$ – Brian Drummond Apr 25 '15 at 13:42
  • \$\begingroup\$ My question is zero mean noise meaning rounding errors but what is the truncation errors ? \$\endgroup\$ – gmotree Apr 25 '15 at 13:46
  • \$\begingroup\$ I understand your good answer but I can't connect between my original question and your answer. \$\endgroup\$ – gmotree Apr 25 '15 at 13:48
  • \$\begingroup\$ Sir, When do i receive your another example? \$\endgroup\$ – gmotree Apr 26 '15 at 5:52

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