th  - 1987 - 51st ENC Conference

WK34
DECONVOLUTION OF HIGH RESOLUTION TWO-DIMENSIONAL
NMR SIGNALS BY DIGITAL SIGNAL PROCESSING WITH"
LINEAR PREDICTIVE SINGULAR VALUE DECOMPOSITION
David Cowburn. Adam E. Schuasheim, and Francis Picart
The Rockefeller University,
New York, New York, 10021
NMR signals from high resolution pulsed experiments can be adequately represented by sums of
sinusoids. Normally these signals are transformed to the frequency domain by FOurier transformation
and the chemical information inherent in the frequency, damping, intensity, or phase of the sinusoids is
subsequently obtained by various deconvolutions, ranging from simple 'peak-picking' for frequency to
non-linear least squares fitting to obtain all the sinusoid properties. This deconvolution in the frequency
domain is particularly compficated by the need to set initial parameters for the non-linear least squares
analys~. The characteristics of the coatribufing sinusoids in the lime domain are needed for recognition
of patterns of signals and correlation with expected properties. We show a new method of analyzing
two-dimensional NMR spectra for this purpose.
The technique of linear predictive singular value decomposition 0..PSVD), applied previously in
NMR (1), permits the extraction of frequency information from a time-domain signal. The technique is
related to the Fourier Transform and presents the same information but in a sometimes more useful
fashion for certain types of processing with some costs in initial processing speeds.
In our approach, a Fourier transform is performed as a digital filter on each row in the tl,t 2 space.
The resulting interferogram is then passed column-by-cohtmn through the LPSVD algorithm. The
information returned from the procedure is stored in a linked-list data file su'ucutre containing the
amplitude, frequency, damping, and phase of the roots extracted for each column as well as a declara-
tion field. A flexible structure is developed which employs a number of routines to process the roots
and remove spurious results.
We have found that these procedures can provide previously unobtainable resolution enhance-
men), and eliminate sinc modulation caused by signal truncation. The procedure can obviate the need
for t l-phase sensitive detection, and can substantially increase the apparent SNR of final spectra. Addi-
tionally, the automated exwaction of chemical information can be facilitated by virtue of the resulting
linked list of roots. These points are illustrated here with both simulated data and simple sets of experi-
mental data.
Acknowledgments
Supported by grants from NSF, NIH, the Keck Foundation, and an equipment grant from Sperr3'
Corporation. We are grateful to Dr. Dennis Hare, and to Dr. R. De Beer for provision of source codes
for their programs, and Computing Services, Rockefeller University, for advice.
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(1). H. Barkuijsen, R. de Beer, W. M. M. J. Bovee, and D. van Ormondt J. Magn. Res. 61 465-