Signal/noise ratio definition

Limit of Detection (LOD) The smallest signal attributable to the analyte according to specified criteria that vary from statistical definitions to a specified signal/noise ratio (Section 8.4.1) together with requirements to ensure analyte identity, i.e., to ensure that the measured signal can be attributed to the target analyte and only to that analyte. Instrumental LOD refers to detection of pure analytical standard in clean solvent, and method LOD to blank matrix spiked with standard analyte and subjected to the complete analytical method. 

The simplest and most intuitively obvious definition of LOD is the lowest concentration (or amount) of analyte for which the observed signal/noise ratio (S/N) = Z, where Z is (somewhat arbitrarily) chosen to be in the range... 

The simplest definition of sensitivity is the signal-to-noise ratio. One criterion for judging the sensitivity of an NMR spectrometer or an NMR experiment is to measure the height of a peak under standard conditions and to compare it with the noise level in the same spectrum. Resolution is the extent to which the line shape deviates from an ideal Lorentzian line. Resolution is generally determined by measuring the width of a signal at half-height, in hertz. 

Signal-to-noise ratio characterizes recorded signals and signal functions with regard of their quality, i.e., their precision. Unfortunately, the signal-to-noise is not uniformly used in analytical chemistry. In addition to the definitions given in Eqs. (7.1) and (7.2), there exist another one, related to the peak-to-peak noise Npp ... 

It is difficult to comprehend why this measure has not been applied in analytical chemistry. Instead of this, in the last decades the signal-to-noise ratio has increasingly been used. Signal-to-noise ratio, see Eq. (7.1), is the measure that corresponds to r in the signal domain. In principle, quantities like S/N (Eq. (7.1)) and / (Eq. (7.7)) could represent measures of precision, but they have an unfavourable range of definition, namely range[r = range[S/N] = 0... oo. 

For purposes of quality control, any cell preparation used in the screen (see below) needs to have a definitive or consensus diagnosis and grading determined by histological examination. Furthermore, tumor cell preparations must be at least 80% tumor cells (as determined by cytopathological examination), whereas normal cell preparations must be devoid of any tumor cells. Cell viability, determined by trypan-blue exclusion, must be a minimum of 70%, and the signal-to-noise ratios for a predetermined cell cluster concentration must be at least threefold. 

Definition The signal-to-noise ratio (S/N) quantifies the ratio of the intensity of a signal relative to noise. 

In many analytical applications a signal-to-noise ratio of 3 (sometimes 2) is used as definition of detection limit... 

Assuming that the noise is white noise, that is, S f) = S0, Eq. (18) is simplified and the signal-to-noise ratio is determined from Eqs. (17) and (18). Equation (18) is simplified by the definition of the noise-equivalent power (in watts per Hz1/2)... 

Limit of Quantification For the limit of quantification, or limit of determination, definitions and formulas are very similar to those of LOD, except that for LOQ, is taken to be 5, 6, or even 10 [2, 4,15, 56,72, 96]. A value of 10 for means that the %RSD at the limit of quantification is 10%. The LOQ thus corresponds to that concentration or amount of analyte quantifiable with a variation coefficient not higher than 10% [98]. The LOQ is always higher than the LOD and is often taken as a fixed multiple (typically 2) of the detection limit [4]. Also, the determination limit is referred to as the signal 10 times above the noise or background signal, corresponding to a signal-to-noise ratio of 10 1 [72, 85]. 

It is important to specify detectors independent of column parameters and of sample size. One parameter that does this is minimum detectable level, MDL. It is the "level" of sample in the detector at the maximum of the peak, when the signal-to-noise ratio is two. The term detectability is sometimes used for MDL. Variations of this definition are sometimes given which require the signal-to-noise ratio to be either one, three, or five. The parameter is also defined sometimes in terms of root-mean square (rms) noise. Peak-to-peak noise can be taken as six times rms noise. 

Detector sensitivity is best explained in terms of signal to noise ratio, which is the minimum detectable quantity with a signal to noise ratio of two (Willard, 1988). Detector sensitivity is linked to the method detection limit, a concept that we routinely use in environmental project work. (The definitions of detection limits in environmental pollutant analysis are discussed in Chapter 4.5.1.) The MDLs, however, while being related to detector sensitivity, greatly depend on the analytical method, sample matrix, and the analyte itself. In this chapter, we will address detector sensitivity in relative terms by comparing sensitivities of various chromatography detectors. 

LoDs shown in Table 6.7 were compared with those of Table 6.8 obtained two years earlier based on three times the signal-to-noise ratio (S/N). It should be noted that this old definition of LoD based on 3 S/N is not equivalent to the IUPAC definition of LoD. One might conclude that the results of LoDs calculated with the ISO 11843 methodology are slightly higher than, but still comparable with, LoDs based on 3 S/N. 

Sensitivity the sensitivity of an instrument is the ratio of the ionic current change to the sample flux change in the source (in Cqg-1). The analytical sensitivity is the smallest quantity of compound yielding a definite signal-to-noise ratio, often 10 1. 

One of the attractions of flame atomic absorption is that relative standard deviations are often better then 1% in ideal situations and only marginally poorer than this when lower levels are being analysed. By definition the precision of measurement is 50% relative standard deviation at the detection limit, because it is at this point that the signal to noise ratio equals 2. 

No definitive conclusion can be made yet because we caimot firmly rule out the possibility that the detected copper and zinc are from the background methanol catalyst. Moreover, the poor signal-to-noise ratio does not allow us to look at the correlation of Cu and Zn accumulation in alumina to the loss of its activity. Efforts are being made to circumvent the background interference by analyzing the thin film prepared from spent alumina particles with TEM. 

Spectral smoothing increases the signal-to-noise ratio of the spectrum at the expense of resolution. Thus, while smoothing produces smoother looking bands, some information content may be lost. Furthermore, it may cause changes in the measured peak position and band shape. Interpolation represents the inverse of smoothing. That is, the resolution is artificially enhanced to provide a better definition of band shape. This may be achieved by polynomial fitting of the spectral data points. 

When using linear calibration models, the calculations of signal to noise ratio, selectivity and sensitivity are easily obtained in accordance with lUPAC standard definitions. The calculation of confidence limits is also achievable using the following equation [5] ... 

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