Signal-to-Noise Ratio Considerations

The SNR is a figure of merit that is frequently cited in product literature. Values are often reported as peak-to-peak absorbance measured for a given spectrometer configuration over a specified time period and spectral range and at a specified spectral resolution. The SNR varies in direct proportion to the instrument throughput, source spectral radiance, detector D, and spectral resolution [35]. SNR also increases with the square root of measurement time which 

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For concentrated or bulk samples a transmission experiment is both the simplest and the most effective. In essence, one measures the X-ray intensities incident and transmitted through a thin and uniform film of the material. Careful analysis of signal-to-noise ratio considerations indicates that optimal results are obtained when the sample thickness is of the order of 2.5 absorption lengths. Since in this case a simple Beer s law applies, the data are usually plotted as In(7//0) versus E. The intensities are measured using ionization chambers in conjunction with high-gain electrometers (see Fig. 11). 

In fig. 2 an ideal profile across a pipe is simulated. The unsharpness of the exposure rounds the edges. To detect these edges normally a differentiation is used. Edges are extrema in the second derivative. But a twofold numerical differentiation reduces the signal to noise ratio (SNR) of experimental data considerably. To avoid this a special filter procedure is used as known from Computerised Tomography (CT) /4/. This filter based on Fast Fourier transforms (1 dimensional FFT s) calculates a function like a second derivative based on the first derivative of the profile P (r) ... 

Sensitivity by itself is not sufficient to completely evaluate an LCEC system for analytical purposes. The minimum detectable quantity (detection limit) is of more practical importance. The detection limit takes into consideration the amount of baseline noise as well as the response to the analyte. The detection limit is then defined as the quantity of analyte which gives a signal-to-noise ratio of three (a S/N of 3 is the generally accepted criterion although other values have been used). For a complete description of an LCEC application, both the sensitivity and detection limit, along with the S/N criteria used, should be provided. 

Response Of course we used noise-free data. Otherwise we could not be sure that the effects we see are due to the characteristics we impose on the data, rather than the random effects of the noise. When anyone does an actual, physical experiment and takes real readings, the noise level or the signal-to-noise ratio is a consideration of paramount importance, and any experimenter normally takes great pains to reduce the noise as much as possible, for just that reason. Why shouldn t we do the same in a computer experiment ... 

The advantages of CC in ultra trace analysis are shown to be unmistakable. The quantitative reliability of the method was demonstrated by the extension of a calibration graph for phenol to two decades of concentration more when compared with conventional chromatography. A considerable improvement of the signal-to-noise ratio can be achieved in a relatively short time. The method offers excellent prospects for ultra trace analysis in cases where preconcentration of the solute fails. 

Theoretical considerations shown in the above equation also indicate that peak area precision is inversely proportional to the peak sig-nal/noise ratio, and to the number of sampling points across the peak width. For very noisy peaks, the peak area precision is limited by random noise fluctuations (Figure 6). Figure 7 shows that the precision of the peak area degrades rapidly when the signal-to-noise ratio is less than 100. Statistical considerations also stipulate a minimum data sampling... 

For LC peaks at 0.1% level or less, a considerably long acquisition time may be required to achieve suitable signal-to-noise ratio. A couple of analytical techniques may be used to concentrate the degradants before the LC-NMR analysis, such as column switching or solid phase... 

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