Temporal Pulse Compression Beyond the Fourier Transform Limit
Bibliographic record
Abstract
It is a generally known that the Fourier transform limit forbids a function and its Fourier transform to both be sharply localized. Thus, this limit sets a lower bound to the degree to which a band-limited pulse can be temporally compressed. However, seemingly counterintuitive waveforms have been theoretically discovered, which, across finite time intervals, vary faster than their highest frequency components. While these so-called superoscillatory waveforms are very difficult to synthesize due to their high amplitude sidebands and high sensitivity, they open up the possibility toward arbitrarily compressing a temporal pulse, without hindrances from bandwidth limitations. In this paper, we report the design and realization of a class of superoscillatory electromagnetic waveforms for which the sideband amplitudes, and hence, the sensitivity can be regulated. We adapt Schelkunoff's method for superdirectivity to design such temporally compressed superoscillatory pulses, which we ultimately realize in an experiment, achieving pulse compression 47% improved beyond the Fourier transform limit.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".