Application of Odd-Order Derivatives in Fourier Transform Nuclear Magnetic Resonance Spectroscopy toward Quantitative Deconvolution.

When Fourier transform (FT) spectrum peaks are overlapped, primary maxima of odd-order derivatives can be used to evaluate their independent intensities. We studied the feasibility of higher odd-order derivatives on Lorentzian peak shape and magnitude peak shape. Simulation studies for FT nuclear magnetic resonance (NMR) spectroscopy demonstrated good results toward quantitative deconvolution of overlapping FT spectrum peaks. Although it is not so desirable to deconvolute special line shapes such as Gaussian, Voigt, and Tsallis profiles, the odd-order derivatives exhibit a bright future compared to even-order derivatives. An application example of practical NMR spectroscopy with ethylbenzene isomers is presented. White Gaussian noises were added to the simulated spectra at two different signal-to-noise ratios (20 and 40). Kauppinen's denoising and smoothing algorithms can effectively remove interference of the noise and help to have good deconvoluting results using the odd-order derivatives. We compared features of our approach with popular deconvolution sharpening algorithms and conducted a comparison study with Kauppinen's Fourier self-deconvolution. Our approach has a better dynamic range of peak intensities and is not sensitive to the sampling rates. Other common deconvolution methods are also discussed briefly.