Apodization refers to the mathematical processing technique
by which the FID is multiplied pointwise by some appropriate function in order
to improve the instrumental line shape. The term apodize actually derives from its Greek meaning “removing the feet”. The feet being
referred to are actually the side-lobes found in the FT spectrum resulting from
zero-filling a truncated FID (this phenomenon is also known as leakage).
Probably the most widely used apodization function in NMR,
especially in 13C spectroscopy, is the Exponential function although other
functions such as Hanning are also very popular.
In this short post, I want to introduce a new apodization
function, the so-called Stanning
function which gives superior results compared to Exponential and Hanning
apodization functions.
The name Stanning is a play on words which combines Hanning (which
forms the basis of this function) with Stan, the inventor of
this apodization function to whom all credit should be given.
The performance of this apodization function is illustrated
with a 19F NMR spectrum whose FID is shown in Figure 1.
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| Figure 1 |
This FID consisted of ca 59K acquired data points which are
then extended by zero filling to a final size of 128K. As the FID has not fully
decayed to zero during acquisition, resulting FT spectrum will show the
expected truncation artefacts, as shown in Figure 2.
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| Figure 2 |
Multiplication of the FID by an exponential function, in
this case with a line broadening value of 1.0 Hz results in the following
spectrum where the wiggles have been significantly reduced but not in a totally
satisfactory way (see Figure 3).
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| Figure 3 |
Application of the new Stanning function yields the result
depicted in Figure 4. As it can be seen, the truncation artifacts have been
further reduced whilst the resolution of the spectrum is slightly better compared
to the exponential function.
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| Figure 4 |
The mathematical formulation of Stanning as well
as some additional illustrative examples will be covered in a future blog post.
