NMR Processing: Convolution: Exponential Multiplication

 

Function:
 

The figure shows the continuous example FID after em with LB = 0.5; this is dataset fid/101 in the download package.

Purpose:

• The objective of the multiplication of the FID with an exponential is to increase signal-to-noise ratio, at the expense of resolution. A reasonable compromise is the matched filter, where LB is set to the natural linewidth of the peaks.
• Another objective is apodisation, i.e., to cause a faster deacy of the FID in case there is still signal left at the end of the acquisition time.

Examples/Exercises:
 

	Click on the figure to see the effect of em with LB = 1 applied to the synthetic dataset synth/110 in the download package. The increase in signal-to-noise is notable, without significant degradation of resolution. Here, we have applied a matched filter.
	Click on the figure to see the effect of em to cure a clipped FID and to achieve apodisation. With zero filling, a clipped FID causes "ripples" in the spectrum, which can be removed by em. By clicking on the TopSpin icon, you can download the FID to play with a few settings using the FID apod/4 (this is a P-31 spectrum of 85% H3PO4): The FID consists of TD = 1024 points. Set SI = 512 and LB = 0 and perform em to see the FID without zero-filling and without apodization: at the end of the FID there is still a significant signal present; perform ft and pk to transform and phase correct the spectrum using the saved phase constants. You see a strong peak at -2.8 ppm and an artefact (quad image) at 3.6 ppm. Now we do the same again, but this time using zero filling: SI = 1024; after em the FID looks like the red FID in the figure on the left; after em, ft and pk the spectrum shows extensive wiggles due to the clipped FID. Now we are going to cure this clipping using a faster decaying exponential: LB = 100; after em the signal is basically gone at the end of the FID, and after ft and pk the resulting spectrum is relatively free of ripples (a LB = 200 is required to remove them completely).
	Click on the figure to see the effect of em to bring out a weak peak that was hidden in the noise (broadened because of intermediate chemical exchange). By clicking on the TopSpin icon, you can download the FID to reproduce the figure using the FID em_sn/6

Properties:

• No change in lineshape.
• Spectra can still be used for integration.

Literature:

• Hoffman, Levy, Progr. NMR Spectrosc. 1991, 23, 211; doi:10.1016/0079-6565(91)80005-M
• Lindon, Ferrige, Progr. NMR Spectrosc. 1980, 14, 27; doi:10.1016/0079-6565(80)80002-1
• Becker, Ferretti, Gambhir, Anal. Chem. 1979, 51, 1413; DOI: 10.1021/ac50045a016
• Kalinowski, Berger, Braun, C-13-NMR-Spektroskopie, Thieme Verlag, 1984