What's Happening ? (part 3; Visual Weighting)

iNMR offers many (hidden) weighting options, but only 4 window functions are available, apparently, because:

• nobody ever asked for more;
• more options would mainly dilute the goodness of the offer;
• the proliferation of recipes in the past was not justified; researchers have proposed functions for purposes that are better targeted with different treatments, like Linear Prediction, Baseline Correction, Reference Deconvolution or, better, today's digital instruments;
• each of the 4 options contain an adjustable parameter, so you have more than 4 functions: you have 4 families of functions;
• you can combine 2, 3 or 4 functions together, for a total of 15 combinations, assuming they make any sense.

In practice, the exponential and the gaussian function are used for 1D spectra and the sine bells for 2D spectra, but this is not a rule. When we speak of exponentials, we mean both the decaying exponential (negative argument, used for sensitivity enhancement) and the raising exponential (positive argument, used for resolution enhancement). When we speak of gaussian bells, we only mean the classic Gaussian bell. It can be used to reduce noise and artifacts, not for resolution enhancement (actually it's detrimental for resolution). It happens that the raising exponential, the only weight we have to increase the resolution, creates a lot of artifacts and must always be accompanied by the gaussian bell.

The dialog gives you two alternatives: “(+) Sensitivity” and “(-) Resolution”. From the above discussion, if not from their position in the dialog, it should be clear that they refers to the sign of the exponential and nothing else. They could have been called, more accurately, “positive exponential” and “negative exponential”. The chosen nomenclature would hopefully be more informative for the majority of the users, although if it is less precise. If you only want to use the gaussian function, the above choice is utterly ignored. Unless you are looking for special effects, you can, instead, ignore the gaussian slider. I mean: if you are a beginner in the field of NMR processing, there is no necessity of touching that control. You can still achieve good results with the first slider only. The trick is that, in the case of a negative exponential, iNMR will automatically move the bottom slider for you. The following simple formula is used:

movement of the bottom slider = 0.63 x movement of the top slider

The number 0.63 has a weird origin. 0.66 was too much and 0.5 was too little. The programmer that wrote that part of iNMR was born in 1963, therefore he put his signature in this invisible form. If any reader comes to the conclusion that a different fraction is better suited, please write!

If you only have to optimize a single variable, and you have visual feedback, what else is there to say? The math expressions are all in the manual.

The choice at the bottom of the dialog (spectrum / time domain / weight) is only for visualizing purposes. The same dialog also shows the effect and the shape of the (co-)sine bells (but without interaction).

If you are enhancing the sensitivity, you can choose between the two functions, but there is little need of mixing them. Gaussian weighting creates smaller wings, but exponential weighting lets you achieve the matched filter (when the shape of the weight is equal to the shape of the FID: this combination yields the maximum theoretical sensitivity). In conclusion: both choices are valid.
If you are enhancing the resolution, you can obtain the best result by using both sliders. In other words: when you have already mastered the use of the first slider and feel you have squeezed every thing from it, that's the time to learn using the bottom slider.

We have another weapon to increase the resolution, namely Reference Deconvolution. It's much more difficult to handle. Its main reason of existence, in the context of iNMR, is to remove the asymmetry caused by non homogeneous magnetic fields.