When processing NMR data a window function, or apodization, is often applied to the raw data before fourier transformation to enhance the appearance of the spectrum. For one dimensional spectra an exponential multiplication is often used. This window function reduces the noise at the expense of resolution.
Window functions are a way of scaling the data points in raw NMR data to enhance desired features, typically signal-to-noise or resolution. An exponential function retains the intensity of the initial point in the FID but reduces the intensity of later points, with the final point being most reduced. The rate at which the intensity is scaled down is not linear across the length of the FID, but follows an exponential curve specified by the line broadending parameter (LB on Bruker spectrometers).
In the figure below an unmodified FID is shown in purple at the top.
Exponential line broadening of 0.3, 1.0 and 3.0 Hz was applied to this FID and
is shown in the lower traces in green, red and blue. Note how the intensity of
the data points on the right of the FID is reduced as the line broadening is
increased. These later points mainly contribute noise to the spectrum so
reducing their intensity is a way of reducing the noise in the spectrum.
The figure below shows two multiplets in a 1D 1H spectrum. The purple trace at the top was obtained without applying any window function. In the lower traces an exponential multiplication was applied with the line broadening increasing from 0.3 (green) to 1.0 (red) and finally 3.0 Hz (blue). The exponential window smooths out the noise, but the peaks become broader and the resolution is decreased.
Exponential multiplication is good for enhancing signal-to-noise when looking for small peaks in noisy data, but it may hide splitting from small couplings. In many cases, processing the data in multiple ways with different window functions is the best way to obtain the most information from your data.
Acknowledgements
Thanks to Alex Bogdanov for suggesting this topic.
I’ve (we’ve) used more extreme apodization when we had a need to drill down for very small J couplings - close to 0.5 Hz (e.g. hunting for homoalyllic or ‘W’ couplings) - close to twice the natural ‘magnet resolution’. Try a negative exponential, say, LB =-0.5 combined with a a Gaussian say 0..2). Simple Sine bell (SIN =0) gives extreme resolution with distortions at the baseline The key is to experiment with different values of LB and Gaussian until you get the best balance - Ted M
ReplyDelete