th  - 1987 - 51st ENC Conference

WK3C
LINEAR PREDICTION Z-TRANSFORM (LPZ) SPECTRAL ANALYSIS
WITH ENHANCED RESOLUTION AND SENSITIVITY
J. Tang* and J. R. Norris
Chemistry Division, Argonne National Laboratory
Argonne, IL 60439
We have developed a new approach of spectral analysis (LPZ) l"s with improved
resolution and sensitivity by combining the linear prediction (l~P) theory and the
z-transform, a combination of Fourier and Laplace transform. Instead of using the
power spectrum formula obtained by the conventional MEM method, the LPZ
formula should be used to obtain a spectrum with phase information. The linear
prediction coefficients can be calculated by the Householder decomposition
(QRD) 1-~, the singular value decomposition (SVD), the autoregression method (AR)
using the Levinson-Durbin algorithm or the Burg's algorithm s. The LPZ method
can overcome the truncation artifacts and phase distortion problems. Applications
of the LPZ method to I-D and 2-D NMR signals will be demonstrated. In addition,
the comparisons among many variations of the LPZ method (using SVD, QRD or
AR) and the other similar methods such as LPQRD 4, LPSVD s and the ME..M 6"7
methods will be illustrated.
1. J. Tang and J.R. Norris, J. Chem. Phys. 84, 5210 (1986).
2. J. Tang and J.R. Norris, J. Magn. Reson. 69, 180 (1986).
3. J. Tang and J.R. Norris, Chem. Phys. Lett. 131, 252 (1986).
4. J. Tang, C.P. Lin, M.K. Bowman, and J.R. Norris, J. Magn. Reson. 62, 167
(1985).
5. H. Barkhuijsen, J. de Beer, W.M.M.J. Bovee and D. van Ormondt, J. Magn.
Reson. 61, 167 (1985).
6. J.P. Burg, Thesis, Stanford University (1975).
7. S. Sibisi, J. Skilling, R.G. Brereton, E.D. Laue and J. Staunton, Nature 311, a46
(1984).
This work was supported by the Division of Chemical Sciences, Office of B~_~ic
Energy Sciences of the U.S. Department of Energy under contract W-31-109-Eng-38.