4.9 Exercises 4­17
4.9 Exercises
E 4­1
In a spectrum with just one line, the dispersion mode lineshape might be ac-
ceptable ­ in fact we can think of reasons why it might even be desirable
(what might these be?). However, in a spectrum with many lines the disper-
sion mode lineshape is very undesirable ­ why?
E 4­2
Suppose that we record a spectrum with the simple pulse-acquire sequence
using a 90 pulse applied along the x axis. The resulting FID is Fourier trans-
formed and the spectrum is phased to give an absorption mode lineshape.
We then change the phase of the pulse from x to y, acquire an FID in the
same way and phase the spectrum using the same phase correction as above.
What lineshape would you expect to see in the spectrum; give the reasons for
your answer.
How would the spectrum be affected by: (a) applying the pulse about -x;
(b) changing the pulse flip angle to 270 about x?
E 4­3
The gyromagnetic ratio of phosphorus-31 is 1.08 × 108 rad s-1 T-1. This
nucleus shows a wide range of shifts, covering some 700 ppm.
Suppose that the transmitter is placed in the middle of the shift range and
that a 90 pulse of width 20 s is used to excite the spectrum. Estimate the
size of the phase correction which will be needed at the edges of the spectrum.
(Assume that the spectrometer has a B0 field strength of 9.4 T).
E 4­4
Why is it undesirable to continue to acquire the FID after the signal has de-
cayed away?
How can weighting functions be used to improve the SNR of a spectrum?
In your answer described how the parameters of a suitable weighting function
can be chosen to optimize the SNR. Are there any disadvantages to the use of
such weighting functions?
E 4­5
Describe how weighting functions can be used to improve the resolution in
a spectrum. What sets the limit on the improvement that can be obtained in
practice? Is zero filling likely to improve the situation?
E 4­6
Explain why use of a sine bell weighting function shifted by 45 may enhance
the resolution but use of a sine bell shifted by 90 does not.
E 4­7
In a proton NMR spectrum the peak from TMS was found to show "wig-
4­18 Fourier transformation and data processing
gles" characteristic of truncation of the FID. However, the other peaks in the
spectrum showed no such artefacts. Explain.
How can truncation artefacts be suppressed? Mention any difficulties with
your solution to the problem.