Experimental Noise in Data Acquisition and Evaluation.

I. Noise Amplitude Distribution Function on High-Resolution FT-NMR Instruments.
II. Signal-to-Noise Ratio Measurements in NMR.

by Stanislav Sýkora and Juerg Vogt
Scanned from Bruker Report 2/79, pages 15-18, 1979.
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I. The noise reaching the analog-digital coverter of a HR-NMR instrument has been analysed for any deviations from normal distribution. Several statistical normality tests had been employed, such as skewness, curtosis, second and fourth moment and the correlation between them. It has been found that any such deviation, if present at all, is below the threshhold of detection at 95% confidence level. Tentative reasons for this fact are listed. The fact that the noise is indeed normal implies that standard data averaging techniques are indeed the optimal ones and it has no sense to look for better ones.

II. The simple way of estimating the signal-to-noise ratio (S/N) in HR-NMR spectra consists of estimating the height of a standard peak (Ph) and the peak-to-peak amplitude of a segment of the spectrum containing only noise (Na) and setting S/N = 2.5*(Ph/Na). This Note investigates to which extent such a procedure can be considered objective and reliable. The maximum and the minimum of a segment of noise with n data points is a well-defined random variable whose statistical properties can be easily analysed. In particular, its median and quantiles for any confidence level are given by explicit formulae. From these it follows that the standard method is depends too much of the size of the noise segment and should be therefore replaced by a more sophisticated method.

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