Application of Odd-Order Derivatives in Fourier Transform Nuclear Magnetic Resonance Spectroscopy toward Quantitative Deconvolution
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".