Optimization of the Signal-to-Noise Ratio

This noise is due to the thermal motion of the carriers (electrons) in the different resistors used in the photomultiplier. In general, the signal uncertainty caused by this source of noise is much lower than those generated by both dark noise and shot noise. 

In many optical spectroscopy experiments, the intensity of the radiation involved is very low. In these conditions, the noise can be as intense as the signal. The signal-to-noise ratio is the quantity that characterizes the quality of the measured signal. There are several methods that are especially devoted to increasing this ratio. Some of them deal with the measurement procedure, whereas others involve the use of some specific electronic devices to treat the measured signal. The most usual methods employed for the increment in the signal-to-noise ratio are listed next. 

---

A. G. Papavassiliou and D. Bohmann, Optimization of the Signal-To-Noise Ratio in South-Western Assays by Using Lipid-Free Bsa As Blocking Reagent, Nucleic Acids Research, vol. 20, no. 16, pp. 4365-4366, Aug. 1992. 

It would be premature to suggest that optimization of the signal to noise ratio for this type of chemical sensor could be done entirely theoretically. Careful sensor design with respect to electrical and thermal shielding are... 

The detection system should have a gain of approximately 100 dB and an adjustable band width to enable optimization of the signal to noise ratio and reflection of spurious modulations from the detector. 

The time resolution of such experiments is not limited by the rf pulse width. Pulses can be staggered from scan to scan by less than their duration, yet by deconvolution the time dependence can be recovered with a resolution equal to the stagger interval, but this incurs a reduction of the signal-to-noise ratio. As compared to conventional NMR, both flip angle and acquisition time must be optimized in a quite different manner to achieve maximum sensitivity. ... 

This paragraph presents a summary of the most relevant expressions provided by Long et al. [1] for the optimization of thin absorbers (effective thickness / high mass absorption. The result of this work is used in Sect. 3.3.2 of the book. Following the approach of [1], we adopt for the signal-to-noise ratio ... 

In our opinion the signal-to-noise ratio of Taguchi is not a suitable optimization variable. This has two reasons. The first is that R,=0 cannot be handled by this response. The second reason is that situations can result with the same S/N values, while in a chromatographic context these situations are different. As an example, suppose that there are three mixture compositions which result in a signal to noise ration which is doubtful (i.e. S/N < 0.6, Figure 6.3). The first (continuous line) has almost adequate resolutions at all temperatures. The second (dashed line) has reasonable resolutions at 20 °C, but no resolution at 30 °C. The third (dotted line) has reasonable resolutions at 30 °C, but no resolution at 20 °C. In the laboratory 20 °C occurs often, therefore the last mobile phase composition is unacceptable. A choice between the first and the second requires judgement from the researcher. 

Load now the H FIDs of peracetylated glucose D NMRDATA GLUCOSE 1D H GH 010001-012001. FID and Fourier transform the data. Phase the spectra and store them (reference spectra). Note that in this case the signal-to-noise ratio is low for all three spectra and that resolution is not the best for the second and third data set (see Table 5.1). Try to find the best compromise with respect to signal-to-noise ratio and resolution. Use different weighting functions for this optimization and store the results separately. Compare and interpret the results. 

Now load the 64K "C FID of peracetylated glucose D NMRDATA GLLICOSE 1D C GC 001001.FID and apply forward LP to improve the signal-to-noise ratio of the corresponding spectrum. Carefully inspect the FID to define the First Point used for LP and Last Point used for LP and the Number of Coefficients. Follow the rules given before and your experience acquired in the last Check its, perform several calculations varying the LP parameters to optimize the spectral quality. Compare the results with the spectrum obtained with/without applying a matched exponential filter and without LP. 

---