Interpretation of Time-Frequency Distribution Cross Terms
Bibliographic record
Abstract
Noise and vibration signals which are stationary are frequently analyzed for frequency content using Fourier Transform methods. Frequency content can be clearly displayed, but temporal characteristics of signals can easily be obscured in a frequency spectrum. Several commonly available methods of analyzing nonstationary signals are available, such as short-time Fourier Transform and wavelet analysis. Smearing of data in the time and/or frequency domains leads to limited usefulness of these methods in analyzing rapidly varying signals. This also applies to stationary signals with perceivable temporal characteristics. The Wigner Distribution is a time-frequency analysis which can analyze rapidly varying signals and show the effects of rapid changes in signal characteristics. It is appealing because it fully preserves all the information present in the original signal. However, the Wigner Distribution of a measured signal typically contains cross terms which do not correspond to spectral components in the original signal. Much success has been achieved at reducing cross terms by modifying the Wigner Distribution (at the expense of losing some of the original signal information). The objective of this paper is to show that these cross terms contain information about temporal variations of the signal envelope and are not just artifacts of the Wigner Distribution calculation.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.022 | 0.005 |
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".