Chapter 5 The padé-laplace analysis of nmr signals

Publisher Summary This chapter presents an overview of the Pade-Laplace (PL) theory highlighting the most important mathematical properties of the method. Illustrations of PL to the analysis of experimental multiexponential relaxation curves are given to show the performances of the Pade-Laplace treatment. The chapter is devoted to the processing of free induction decay (FIDs) using the PL method, emphasizing the specificities of such a treatment for this particular class of signals. Both simulated and experimental FIDs are presented and discussed to show how PL works in nuclear magnetic resonance (NMR) spectral analysis. The chapter presents the application of the PL method to the extraction of NMR spectral parameters (amplitude, frequency, and linewidth) from both simulated and experimental FIDs. The PL method can be easily associated with an iterative procedure: this procedure consists in introducing the output of the PL computation as starting values in a non linear least-squares method. In this way, the PL method is enriched by the elements of the statistical method although this procedure remains essentially analytic.

[1]  P. Claverie,et al.  Analysis of multiexponential functions without a hypothesis as to the number of components , 1987, Nature.

[2]  I. Gerothanassis.  Methods of avoiding the effects of acoustic ringing in pulsed fourier transform nuclear magnetic resonance spectroscopy , 1987 .

[3]  P. Levoir,et al.  Deconvolution of polymer melt stress relaxation by the Padé-Laplace method , 1993 .

[4]  D. Millar,et al.  Time-resolved fluorescence spectroscopy. , 1996, Current opinion in structural biology.

[5]  I. N. Sneddon.  The use of integral transforms , 1972 .

[6]  Z Bajzer,et al.  Padé-Laplace method for analysis of fluorescence intensity decay. , 1989, Biophysical journal.

[7]  John S. Bowers,et al.  An Assessment of the Padé-Laplace Method for Transient Electric Birefringence Decay Analysis , 1992, Comput. Chem..

[8]  I. B. C. Matheson,et al.  The non-equivalence of Padé-Laplace and non-linear least squares data fitting: A Padé-Laplace bias towards slower processes , 1989, Comput. Chem..

[9]  A. May,et al.  Spectral Line Shapes , 1995 .

[10]  D. Szpiro,et al.  Identification des modèles à fonction de transfert: la méthode Padé-transformée en Z , 1990 .

[11]  Z. Grabowski,et al.  Nitrogen-14 nuclear magnetic resonance of azoles and their benzo-derivatives , 1972 .

[12]  Pade–Laplace analysis in the fitting of multi-exponential nuclear magnetic resonance relaxation decay curves , 1992 .

[13]  Patrick Levoir,et al.  Direct analysis of chemical relaxation signals by a method based on the combination of Laplace transform and Padé approximants , 1987, Comput. Chem..

[14]  Linear prediction in spectroscopy , 1994 .

[15]  P. Claverie,et al.  The representation of functions through the combined use of integral transforms and pade approximants: Pade-Laplace analysis of functions as sums of exponentials , 1989 .

[16]  I. M. Longman.  Computation of the padé table , 1972 .

[17]  Jean Aubard,et al.  Spectral Analysis of Quadrupolar NMR Signals by the Padé-Laplace Method , 1992, Comput. Chem..

[18]  L. Filon.  III.—On a Quadrature Formula for Trigonometric Integrals. , 1930 .

[19]  The extended Padé-Laplace method for efficient discretization of linear viscoelastic spectra , 1993 .

[20]  Jacek Gilewicz,et al.  Approximants de Padé , 1978 .

[21]  Jau Tang,et al.  An alternative to fourier transform spectral analysis with improved resolution , 1985 .

[22]  Padé approximation and linear prediction methods , 1988, Nature.

[23]  P. Levoir,et al.  Application of the pade-laplace method to multiexponential decays : Analysis of chemical relaxation signals , 1985 .

[24]  G. A. Baker,et al.  THE THEORY AND APPLICATION OF THE PADE APPROXIMANT METHOD , 1964 .

[25]  E. Yeramian.  Further analysis of multiexponential functions , 1988, Nature.

[26]  Analysis of low‐resolution, low‐field NMR relaxation data with the Padé‐Laplace method , 1991 .