Fast MinMax energy-based phase correction method for NMR spectra with linear phase distortion

Abstract

This paper addresses the problem of phase correction of dense NMR spectra on the example of the etoxy derivative of the fused heterocyclic system 5,6,10b-triazaacephenanthrylene (TAAP-OEt). A new estimation method for the linear phase correction coefficients is proposed that successfully extends the min-max (minimization of maximum errors) approach of Siegel (1981). Distinctive to the Siegel method, the smallest values of the real part of the discrete Fourier transform (DFT) spectrum are maximized, not for the whole spectrum but only for DFT bins near the peaks selected by anew energy-based criterion. Additionally, the method makes use of two one-parameter optimizations for finding the phase correction line coefficients and not the single two-parameter search. The new method is demonstrated to be precise, fast and robust against additive noise. The method’s properties are verified in comparison with the state-of-the-art algorithms of Chen et al. (2002) and Bao et al. (2013) for laboratory recorded TAAP-OEt FID data and for simulated TAAP-OEt signal consisting of the sum of more than 100 complex damped exponentials. Extensive simulations were also conducted on the set of test signals derived from the TAAP-OEt signal by deterministic and pseudorandom manipulation of its content. The components of the signal model were identified by the Bertocco-Yoshida Interpolated DFT (IpDFT) algorithm with a spectral leakage correction. Simulated signals were embedded in the additive Gaussian noise, and the noise-robustness of all of the algorithms was evaluated. The obtained results demonstrate that the proposed method outperforms the Chen and the Bao algorithms, being more than 100 times faster than the Bao method (for a signal having 216 samples).