Processing NMR Data:
Window Functions
William D. Wheeler, Ph.D.
Department of Chemistry/3838
University of Wyoming
1000 E. University Avenue
Laramie, WY 82071
April 1, 2010
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Trapezoid Window
Trapezoid multiplication is used primarily to remove artifacts due to the truncation of the free induction decay (FID). Truncation arises when the time required
for the FID to reach equilibrium exceeds the acquisition time of the experiment.
The acquisition time is a function of the sampling rate and the number of data
points collected. Truncation is the equivalent of multiplication of the FID by a
step function. The Fourier transform of a step function appears as an oscillation
at the base of a peak. This artifact is quite common in NMR spectra and it
is often referred to as a sinc, or sine(x)/x function. The trapezoid can also be
applied to the beginning of the FID to reduce the effects of pulse breakthrough
and other phenomena.
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Free Induction Decay
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Figure 1: Trapezoid window.
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Exponential Window
Exponential multiplication is probably the most often used window function in
one-dimensional NMR. Its main purpose is to increase the signal to noise ratio
of the data, thus requiring fewer scans to obtain a satisfactory spectrum. The
exponential function gives greater weight to the FID at small time values where
it has the greatest amplitude, and lesser weight to the large time values where
its amplitude decreases into the noise. The Fourier transform of an exponential
yields a signal with a Lorentzian line shape. Since this is also the natural shape of
an NMR resonance, the exponential multiplication does not change its inherent
shape. It does however broaden the resonance and historically, this operation
has been known as line broadening. Exponential multiplication may also reduce
artifacts due to the truncation of the FID, if it is applied aggressively enough.
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Exponential Window
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Figure 2: Exponential window.
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Gaussian Window
Gaussian multiplication is used primarily to change the shape of the lines in the
NMR spectrum. The line shape becomes a mixture of Lorentzian and Gaussian.
The Gaussian line shape tends to be narrower than the Lorentzian, especially
near the base of the peaks, so that a spectrum treated in this manner tends to
show enhanced resolution, at the expense of the signal to noise ratio.
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Figure 3: Gaussian window.
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Shifted Gaussian Window
Shifting the Gaussian function yields increased resolution enhancement, but also
introduces artifacts in the baseline.
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Figure 4: Shifted Gaussian window.
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Sine Window
Sine multiplication also changes the shape of the peaks. The sine is typically
used to enhance the resolution in a two-dimensional spectrum. Its effect is
much the same as the shifted Gaussian. It also suppresses artifacts due to the
truncation of the free induction decay (FID).
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Figure 5: Sine window.
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Shifted Sine Window
The shifted sine function yields features that are similar in some respects to
the Gaussian window, and similar in other respects to the exponential window.
It also will suppress artifacts due to the truncation of the free induction decay
(FID). It is used mostly with two-dimensional data.
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Figure 6: Shifted sine window.
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