> how can I estimate integration errors
> due to noise, using the signal-to-noise
> information (the built-in function SINO),
> on a BRUKER AMX 400 spectrometer, xwinnmr 2.1?
Integration of discrete data is approximated as a sum.
Suppose you integrate through a line with N points. This would be:
Sum(S(f_i), i=1..N) df
where df is the frequency increment per point. A famous theorem states that when
averaging signal, signal grows as N where as noise grows as sqrt(N), so the
integrated noise would be
sigma sqrt(N) df
where sigma is the measured standard deviation of the noise at each point.
As you can see, for there to be significant advantage, the signal S(f_i) must be
greater than noise throughout the line you are integrating.
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