Simultaneous Nonlinear Least Squares Fitting Technique For NMR Spectroscopy

Abstract

A new iterative nonlinear least squares fitting technique is developed to fit the NMR free induction decay (FlD) signals in the time domain. The new technique makes it possible fitting all the parameters, e.g., frequencies, decay factors, amplitudes and phases, simultaneously. The corresponding initial values are obtained by linear prediction singular value decomposition (LPSVD)[ 11, which is a completely automatic process without any manual processing. The application of the new fitting technique yields a list of fitted parameters. Since the fitting process is carried out in the time domain, it is possible to fit truncated signals or the ones with shorter duration without a degradation of the resolution. The new technique also enables one to resolve close and overlapping frequency components which can not be resolved by fast Fourier transform (FFT) alone[2]. The FFT is used to provide initial frequencies for some weak components in case of low signal-to-noise ratio, but only as a complementary procedure.