On Fri, 30 Jun 2000, Doug Crice wrote:
> I'll let one of our mathmaticians answer that one.  When you get to a
> certain point in life, you remember the results but not the derivation,
> especially in statistics.  I believe that the basic problem is that each
> sensor picks up some random noise along with the signal.  So when you
> add up the signal from N sensors you also add up N sets of random
> noise.  When random noise signals are added they get bigger by square
> root of N.  The signal gets bigger by N so signal-to-noise improves
> N/(square root of N).
> I don't know the answer in Winquake.
> Doug

Doug is basically right.  The whole concept revolves around the central
theorem of statistics: "the mean value theorem."  The square root of N term
comes in to describe the "spread" or "deviation" in the data using some kind
of distribution model.  Different distributions are used for different types
of random processes.  All the theorem says is that the variance goes
sufficiently close to zero as the number of samples becomes close to
infinity.  Most random processes have a decreasing spread that goes roughly
as:

spread = constant/sqrt(N)

The constant will depend on other parameters.  Note that this converges very
slowly.  This is the limiting factor in a type of computation called "Monte
Carlo Methods" which use probability and random processes to model or compute
very complicated situations.  They converge too slow for most people's taste
however.  But we use this method to calculate the 3-D FFT integral for
transmission electron microscopy to get a good estimate of the brightness for
diffraction spots.  Anyways...

John Hernlund
E-mail: hernlund@.......
WWW: http://www.public.asu.edu/~hernlund/

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