Friday, 7 December 2007

Automatic Processing & SNR

Manuel Perez brought to my attention a possible drawback of the automatic processing scheme for 13C NMR spectra I proposed in my previous post. Basically, his main concern was that small peaks in spectra with low SNR could get suppressed when this procedure is applied.
Of course, he is absolutely right if the method is carried out exactly as it has been described in my post. The problem is that I believe my post was somewhat misleading in the sense that it stated that the weighting functions to be applied should be just a linear ramp combined with a cosine bell function. Whilst this is correct, it’s not enough!. One should not forget that, usually, 13C NMR spectra are weighted with exponential functions in order to improve sensitivity, in particular when the SNR is not very good (as it often occurs). When such a function has to be used, it should also be applied in the automatic processing method I have proposed! Do not forget that a sine-like apodization function does not have the same sensitivity enhancement power as an exponential function does.
Because of the linear ramp employed, the sensitivity of the f-domain spectrum gets poorer and the cosine bell (or 90º shifted sine bell) function is introduced in order to somehow compensate for the decrease of the SNR caused by the linear ramp function. However, this does not mean that an exponential function must not be applied to further increase the SNR as it would be the case of routine 13C NMR processing.So, for example, when using Mnova, one should activate the following weighting functions:

It is important to note that merging of several apodization functions in this way it’s possible because weighting is a linear operation (as is the convolution process).

Let’s take a real-life example which will illustrate some of the points I’ve been talking about in the last two posts. In the figure below I show a 13C spectrum:

We can appreciate a very bad baseline and the intense solvent (Methanol-D4) peaks. For convenience, I will first get rid of the solvent lines by means of the cutting tool available in Mnova (note that this is just a visual tool, the peaks are not physically removed from the spectrum).

Baseline correction could seem quite tricky in this spectrum but it’s not. A polynomial baseline correction with an order higher than 4 or the Whittaker Smoother method included in Mnova will do the job very efficiently as it’s depicted below

Other operations that have been applied to this spectrum were (1) exponential weighting of 1 Hz and (2) phase correction. This is just the standard way to process this kind of spectra.
Now I will apply the ‘automatic’ method. First I will apply the linear ramp and cosine bell weighting function (excluding the exponential one) just to show the issue raised by Manuel. Remember the processing requirements:
  1. Apodization: Linear Ramp + Sine Bell 90º
  2. Magnitude calculation after FT

This is the resulting spectrum. It’s evident that the SNR has decreased significantly and several peaks get suppressed. The point to remember here is that the exponential weighting function has been excluded.

Let me introduce the exponential function again (in combination with the linear ramp and Sine Bell 90º functions) but this time I will use a line broadening value of 3 Hz. Take a look at the new spectrum stacked on top of the spectrum processed with the standard method:

Now the SNR is comparable with the ‘normal’ spectrum and no peaks are missing, whereas the resolution of both spectra is very similar.

I hope that things are clearer now. Should anyone out there find any other problem with this method or just want to give his feedback about it, I will be more than happy to respond.


old swan said...

I have not used the method and I am not going to. While the trick can be useful in some instance, it's not suitable for routine use.
First problem: one day you suggest the use of a sine bell, the day after you suggest the cosine bell. The doubt you are enforcing into the user is already discouraging enough. Applying the standard processing is more straightforward.
Second problem: the sine bell. If the acquisition time is 10 times longer than the apparent T2, the sine bell will cancel the peaks. This means that the method is sensitive to the acquisition time length. Exponential multiplication has no such a limitation. Another consequence is the destruction of broad signals (which can actually be a virtue...).

Carlos Cobas said...

First of all, I have to admit that I made an error when writing this post. I always meant to use a shifted sine bell (90º) function rather than the unshifted version. It’s evident that the idea of using this function (shifted sine bell) was to minimize the SNR reduction caused by the application of the linear ramp function. This was demonstrated in my next post in which I proposed to use the exponential function in combination with the cosine bell (or 90º Sine Bell). The problem was whilst I had in mind the cosine bell function (or the squared counter part) I wrote in the text the sine bell function (and I even plot it) which is obviously completely wrong as it will further decrease the SNR. Now I have amended both the text and the picture. Thanks for pointing this problem out.

Having said that, I do not agree with your comment that the method is not suitable for routine use. I believe it's very convenient for routine 13C NMR(not for 1H NMR as it was clearly stated in the post)

old swan said...

I could not comment what was into your head. I commented what had been written and, mainly, what had been drawn. If you are using a cosine bell, then things are different and your idea is a good one. Still I think that this kind of processing can give different results with different acquisition times. You can probably find that there is an optimal acquisition time / T2 ratio. The same happens with exponential multiplication: there is not a single optimal broadening; the ideal value is proportional to the T2 of the spectrum to be weighted.

Carlos Cobas said...

Yes, you're right, you cannot know what I had in mind, that was my fault, though I think the error was quite evident (In particular if you read my next post on the subject). So I can confirm that the method uses a cosine bell function (actually the square version. Furthermore the 4th power could give better results!)
In fact, the method can be further improved by calculating an average T2* value from the FID (which is possible by using explicit formula) .