Image Processing Reference
In-Depth Information
12.3
TIME-DOMAIN PREPROCESSING
The acquired FID is noisy and not suitable for direct analysis. Due to several
acquisition problems, the resulting FID may be distorted from the ideal curve of
Equation 12.1. The causes of these distortions include, among others, field inho-
mogeneity, the truncation of the FID data before the signal has decayed below
the noise level, unavoidable delay between the RF pulse and the first FID sample,
as well as presence of unwanted broadband resonance. Therefore, acquired FID
is usually preprocessed before the parameters of interest can be estimated. A brief
description of common preprocessing methods applied to FID data is presented
in the following subsections.
12.3.1
Z
F
ERO
ILLING
This is a common procedure in signal processing known as
zero padding
. The
number
of sampled points is increased by adding (padding) zeros at the end
of data series. In general, the procedure is required to fit the fast Fourier transform
(FFT) criterion (number of data points must be a power of two for computational
efficiency); in MRS, zero filling is applied when the acquisition time has been
kept short because of some practical constraints (in this case, few data points
being available) or when signal terms have already decayed below the noise level
and further sampling would add only noise. Adding zeros has the effect of
interpolating extra points into the spectrum and improving its digital resolution
(i.e., the frequency interval between data points). Because adding zeros does not
add extra information to the data, the final result is merely an apparent improve-
ment of spectral resolution used for visualization purposes, which does not
increase the frequency resolution.
N
12.3.2
W
INDOWING
Prior to FFT, the FID signal is usually windowed by multiplying it by a given
function
) with known characteristics. The aims of this procedure can be
different — including either the improvement of signal-to-noise ratio (SNR), or
a better spectral resolution, or the removal of truncation artifacts. In the following
text, it will be shown how the selection of
g
(
t
g
(
n
) may produce different effects on
the absorption-mode spectra. Let us assume
g
(
n
) to be an exponential function
gn
()
=
e dn
. Multiplying the acquired FID by
g
(
n
) and excluding the noise term,
o
we obtain
K
xngn
()()
=
ae e
k
(12.5)
j
φ
((
−++
d
d
)
j
2
π
f
)
n
k
k
0
k
k
=
1
Thus, the resulting curve maintains the original lineshape, but the spectral
line width is increased by a factor
d
(line broadening). The effect is to increase
0
the SNR as shown in Figure 12.2b : data points at the beginning of FID, including
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