Matched filtering a gravitational wave pulsar signal involving reciprocal gamma functions
Bibliographic record
Abstract
The direct detection of Gravitational Waves (GW) is a challenging problem that involves elaborate experimental and data analysis techniques. The verification of a detected signal demands an effective way to distinguish the source signal from the background noise. One possibility is to perform matched filtering analysis using different templates. Matched filtering, a form of pattern recognition, is ubiquitous and finds innumerable and diverse applications. In the present work, we develop the matched filter analysis for a Fourier transformed, monochromatic, Doppler shifted, continuous GW pulsar signal, which incorporates the effects of the rotational and orbital motion of the Earth. The GW pulsar signal involves a product of the reciprocals of two Eulerian gamma functions containing the Fourier transformed bandwidth frequency in their arguments. We derive an exact analytic solution for the case of constant spectral noise density for the inner product of the template with a received signal, thereby obtaining a closed form expression for the fitting factor, a measure of how well the template matches the received signal. This result can in turn be used to determine the location of the GW source. Simpler cases of the spectral noise density for the French-Italian VIRGO GW detector and its special case for Gaussian white noise are also amenable to an analytic formulation. Our analysis shows that the fitting factor may exhibit simple symmetries with respect to the polar direction angle to the source. Approximate symmetries will also be useful in reducing the numerical computation times. Our current study confirms that the whole analysis lends itself well to parallel computation.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| 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) | 0.002 | 0.001 |
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".