When I announced my new blog, a colleague of mine told me that he felt very sceptical about blogs, as they used to be overwhelming and very dilute in general at the same time. I have to admit that I shared the same opinion but I think I’m changing my mind, slowly but at a steady pace. One reason for this change is that since I posted my first blog, I found that it caught the attention of many people and even though there are no public comments in the blog (I guess people don´t like to create Google or Blogger accounts), I have received a few emails with very good and interesting feedback, which will also be useful for future work on software.

For example, regarding Resolution Booster, I was asked about this:

So, why should I use Resolution Booster and not apodization?

First, let me say that I think that a discussion about the correct use of terms such as ‘Apodization’, ‘Weighting Function’, ‘Window Function’, etc, would be worth another blog entry, and maybe I’ll do it soon (unless someone else blogs about it before I do - Stan, are you there?) but for the time being I just want to compare the Resolution Booster algorithm with resolution enhancement algorithms traditionally used in NMR.

OK, in answer to the question, there are several aspects in which I believe Resolution Booster is superior, namely:

For example, regarding Resolution Booster, I was asked about this:

So, why should I use Resolution Booster and not apodization?

First, let me say that I think that a discussion about the correct use of terms such as ‘Apodization’, ‘Weighting Function’, ‘Window Function’, etc, would be worth another blog entry, and maybe I’ll do it soon (unless someone else blogs about it before I do - Stan, are you there?) but for the time being I just want to compare the Resolution Booster algorithm with resolution enhancement algorithms traditionally used in NMR.

OK, in answer to the question, there are several aspects in which I believe Resolution Booster is superior, namely:

- It is easier to use
- It performs better (yields greater resolution enhancements)
- It generates less artifacts
- It eliminates the need for baseline correction
- It can be applied selectively to different areas of the spectrum

That´s a lot of claims. Let me write a little bit about each one of them:

(1) Resolution Booster is easier to use. I write this because with this algorithm there is no need to tune two parameters (as is the case with the Lorentzian-Gaussian function). Resolution Booster requires only one parameter to be optimized, the so called “Line Width” Parameter (there is a second parameter, Threshold, but it can be safely ignored in nearly all routine NMR experiments).

The Line Width parameter should correspond, approximately, to the natural line width, though it does not need to be very precise: making it smaller increases resolution and noise, making it larger goes in the opposite direction. However, a +/-50% deviation (and probably more) from the natural line widths is perfectly tolerable, and this also means that it is relatively easy to automate the selection of this parameter, making the algorithm even more accessible to the not-so-confident user.

(2) In general, the Resolution Booster algorithm yields a greater resolution enhancement than other methods.

(3) Traditional Resolution enhancement methods (e.g. Lorentzian-Gaussian) may introduce wiggles in the baseline because of the rapid truncation of the data that occurs in the tail of the FID with the application of the noise-reducing (Gaussian) function. As can be appreciated in the figure below, Resolution Booster does not present such artefacts, yielding cleaner spectra (note also in this figure the illustration of the point made above, about the greater resolution enhancements achieved with the algorithm)

(4) Spectra processed with Resolution Booster do not require baseline correction. It’s worth mentioning that none of these resolution enhancement techniques are well suited for quantification purposes. Some of these procedures change the intensity of the first points in the FID and thus proper values for integrals are not guaranteed. As for Resolution Booster, it can also change relative intensities. On isolated lines, in principle, it is approximately proportional to the second derivative which, when all lines have the same line width (as they often do) is proportional to the line height. However, broad lines can get suppressed and unresolved humps and shoulders get resolved, which is a positive thing, but their intensities and, to some extent, positions cannot be trusted.

(5) The Resolution Booster algorithm can be signal selective, and this is one of the main advantages to my mind. What I mean by this is that traditional resolution enhancement procedures are usually applied in the time domain by multiplying the FID by an appropriate function. In principle, this operation could be applied in the frequency domain by convolving the corresponding convolution kernel with the frequency domain spectrum. However, from a computational standpoint, the multiplication of the two functions on the time domain followed by a Fourier Transform is more efficient than the convolution of the two functions in the frequency domain (convolution is a more computationally expensive operation than a multiplication).

This implies that it’s not possible (or at least it’s not straightforward) to choose spectral windows (regions) in which the resolution enhancement procedure will act while leaving the other regions untouched.

Resolution Booster is capable of doing such a thing: it allows the user to easily apply it to specific regions and with different parameters, in such cases, for example, when a spectrum has peaks with different line widths (maybe due to exchange or coupling to 14N)

To illustrate this point, in the following figure I’m showing a simulated spectrum with 3 AB systems with different line widths each (10, 5 & 1 Hz) and different J(AB) (10, 5 & 1 Hz respectively). It’s possible to use the Resolution Booster to optimize the resolution individually for every AB system having different line widths by simply selecting the optimum parameter for each spectral region

An invitation

In the example above I have used a synthetic spectrum, mostly because I don’t have at hand any good experimental data sets (nor better ideas). From this blog I would like to invite you to find a real-life experiment in which this technique could be applied for real-life problems. Just drop me an email or post a comment in the blog.

(1) Resolution Booster is easier to use. I write this because with this algorithm there is no need to tune two parameters (as is the case with the Lorentzian-Gaussian function). Resolution Booster requires only one parameter to be optimized, the so called “Line Width” Parameter (there is a second parameter, Threshold, but it can be safely ignored in nearly all routine NMR experiments).

The Line Width parameter should correspond, approximately, to the natural line width, though it does not need to be very precise: making it smaller increases resolution and noise, making it larger goes in the opposite direction. However, a +/-50% deviation (and probably more) from the natural line widths is perfectly tolerable, and this also means that it is relatively easy to automate the selection of this parameter, making the algorithm even more accessible to the not-so-confident user.

(2) In general, the Resolution Booster algorithm yields a greater resolution enhancement than other methods.

(3) Traditional Resolution enhancement methods (e.g. Lorentzian-Gaussian) may introduce wiggles in the baseline because of the rapid truncation of the data that occurs in the tail of the FID with the application of the noise-reducing (Gaussian) function. As can be appreciated in the figure below, Resolution Booster does not present such artefacts, yielding cleaner spectra (note also in this figure the illustration of the point made above, about the greater resolution enhancements achieved with the algorithm)

(4) Spectra processed with Resolution Booster do not require baseline correction. It’s worth mentioning that none of these resolution enhancement techniques are well suited for quantification purposes. Some of these procedures change the intensity of the first points in the FID and thus proper values for integrals are not guaranteed. As for Resolution Booster, it can also change relative intensities. On isolated lines, in principle, it is approximately proportional to the second derivative which, when all lines have the same line width (as they often do) is proportional to the line height. However, broad lines can get suppressed and unresolved humps and shoulders get resolved, which is a positive thing, but their intensities and, to some extent, positions cannot be trusted.

(5) The Resolution Booster algorithm can be signal selective, and this is one of the main advantages to my mind. What I mean by this is that traditional resolution enhancement procedures are usually applied in the time domain by multiplying the FID by an appropriate function. In principle, this operation could be applied in the frequency domain by convolving the corresponding convolution kernel with the frequency domain spectrum. However, from a computational standpoint, the multiplication of the two functions on the time domain followed by a Fourier Transform is more efficient than the convolution of the two functions in the frequency domain (convolution is a more computationally expensive operation than a multiplication).

This implies that it’s not possible (or at least it’s not straightforward) to choose spectral windows (regions) in which the resolution enhancement procedure will act while leaving the other regions untouched.

Resolution Booster is capable of doing such a thing: it allows the user to easily apply it to specific regions and with different parameters, in such cases, for example, when a spectrum has peaks with different line widths (maybe due to exchange or coupling to 14N)

To illustrate this point, in the following figure I’m showing a simulated spectrum with 3 AB systems with different line widths each (10, 5 & 1 Hz) and different J(AB) (10, 5 & 1 Hz respectively). It’s possible to use the Resolution Booster to optimize the resolution individually for every AB system having different line widths by simply selecting the optimum parameter for each spectral region

An invitation

In the example above I have used a synthetic spectrum, mostly because I don’t have at hand any good experimental data sets (nor better ideas). From this blog I would like to invite you to find a real-life experiment in which this technique could be applied for real-life problems. Just drop me an email or post a comment in the blog.

## 4 comments:

The middle picture is intriguing. I mean the one where the ppm scale goes from 5.02 to 4.88. Initially se wee 4 unresolved symmetrical triplets. (We know that all NMR signals are symmetric, unless they are a combination of different signals).

The traditional Lorentz-Gauss weighting function enhances the resolution without changing the number of lines. The resolution booster reveals a new ANOMALOUS splitting in all the multiplets. I am saying "anomalous" because the symmetry is broken.

If the splitting can be rationalized, then the RB is a wonderful weapon in our hands. If not, then you'd better warn the reader that RB can easily create peaks from nothing or cancel peaks with the same ease.

Well, the sine bell does something similar, but it's more symmetric and a little more natural.

You wrote:

We know that all NMR signals are symmetricThis is just not true. Many (strong coupled) spin systems are not symmetric. Consider, for example an AB3 spin system, can you say it's symmetric?

You know what I mean: first order multiplets in liquid phase. Without being generic: in your picture the RB reveals an hidden splitting. Is it authentic or is it an artifact? It looks like the latter, because of the asymmetry, but I can't exclude another reason. Maybe you remember the origin of the spectrum..

Dear Carlos, I am experimenting with Res Boost and I have real life example of peaks of different line width. The problem I do not know how to apply it separately for each segment of the spectra. When I am new to Mnova and when ever i use Res Booster, the resolution is changed for the whole spectra. Any help?

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