A peak fitting method for 29Si nuclear magnetic resonance spectra based on singular spectral analysis

Solid-state ²⁹Si Nuclear Magnetic Resonance (NMR) is commonly used in the detection of silicate molecular structure. However, noise in ²⁹Si NMR spectra (NMRS) disturbs the judgment of characteristic peak, thereby affecting the determination of molecular structure types of silicates. A method of peak fitting based on Singular Spectrum Analysis (SSA) is proposed in this paper accordingly. SSA is adopted to determine the position of characteristic peaks and Gaussian fitting model (GFM) is applied to fit characteristic peak in the method, thereby realizing a quantitative analysis of ²⁹Si NMRS. When SSA is applied, the embedding dimension m determines its accuracy. However, the methods for determining m, such as correlation dimension (GP) and False Nearest Neighbors (FNN), often fail because of the differences in the shape of ²⁹Si NMRS. Therefore, two-step greedy (TSG) is proposed to determine the embedding dimension m in the paper. The accuracy of TSG can be respectively improved by 350.7% and 366.8% compared with GP and FNN according to example verification, and the method can accurately determine the embedding dimension m. The peak fitting method (TSG-SSA-GFM) is formed by combining TSG, SSA, and GFM. The experimental results show that the average error of the characteristic peak location is 0.09ppm, and goodness of fit is 99.75%. The method has good accuracy. Therefore, the study provides an important method for the quantitative analysis of ²⁹Si NMR.