Digital Signal Processing Reference
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uration pulse introduces many phase distortions, which then cause the
algorithm to decompose the water resonance into many ICs instead of
just one.
The fastICA results are somewhat less convincing; indeed the algo-
rithm introduced spectral distortions such as inverted multiplets, hardly
visible on the figures presented, that not observed in the analysis with
the GEVD method using a matrix pencil. This is of course an important
issue concerning an automated water artifact separation procedure, as
any spectral distortions might result in false structure determinations
using these 2-D NOESY data.
Spectra of the protein RALGEF
As a second data set 2-D NOESY spectra of the protein RALH814 were
analyzed as well. The data were analyzed with the matrix pencil method
as described above. This time both correlation matrices had the dimen-
sion (128
128) and all 2048 data points were used to estimate the
expectations within the correlation matrices. Again the second correla-
tion matrix R 2 of the matrix pencil corresponded to a bandpass-filtered
version of the correlation matrix R 1 . Figure 14.3 shows an original pro-
tein spectrum with the prominent water artifact, its reconstructed ver-
sion with the water artifact separated out, and a spectrum difference
between original and reconstructed spectra.
An equally good separation of the water artifact could have been
obtained if the correlation matrix R 2 had been calculated by estimating
the corresponding expectations with the low-frequency samples, those
with shifts below the water resonance, of the spectrum only (see figure
14.4(a)). Again the data were analyzed with the FastICA algorithm as
well yielding comparable results (see figure 14.4(b)). However, though
hardly visible on the figures presented, the FastICA algorithm intro-
duced some spectral distortions that had not been observed in the anal-
ysis with the GEVD method using a matrix pencil. This is of course
an important issue concerning an automated water artifact separation
procedure, as any spectral distortions might result in false structure de-
terminations using these 2-D NOESY data.
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