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.