The effects of finite rectangular pulses in NMR: Phase and intensity distortions for a spin‐1/2
Bibliographic record
Abstract
Abstract Pulses in NMR spectrometers have a finite length, but the usual hard‐pulse assumption ignores it, and treats the pulse as a rotation of the frame of reference about the direction of the radiofrequency (RF) magnetic field. However, at frequency offsets comparable to the size of the RF field, there are substantial distortions, mainly in the phase of the signal. This effect is well known and can be easily calculated to show that, despite the complex geometry, the phase distortion is almost linear with the offset. This means that it can be corrected by a first‐order phase correction or by small corrections to pulse‐sequence timing. In this article, we give an analysis of these effects. The deviations from a linear phase correction are analyzed for a general rectangular pulse and illustrated with experimental spectra. The split‐operator approximation for the evolution of this system provides a mathematical foundation and a useful method for this analysis. Furthermore, the relationship between the exact behavior of a signal is compared to the Fourier transform of a rectangular pulse. For typical offsets, the match between these approaches is not good, but it improves as the offset increases. Overall, the detailed analysis of the finite pulse effects gives exact results of the response of a spin system, but also some mathematical and physical insights. © 2009 Wiley Periodicals, Inc. Concepts Magn Reson Part A 34A: 305–314, 2009.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".