Peak-constrained least-squares half-band filters and orthogonal wavelets
Bibliographic record
Abstract
To recall, Cooklev (1995) made some extensions to the Bernstein polynomial method of Caglar and Akansu (1993) for the design of regular half-band filters leading to orthogonal wavelets. However, the ad hoc methodology of Cooklev had many shortcomings which we eliminate by expressing the problem in the form of a quadratic programming problem with linear inequality constraints. This problem is solved with the Goldfarb-Idnani (1983) algorithm, and the methodology we adopt allows for the minimization of half-band filter stopband energy while simultaneously upper bounding the stopband response. This allows us to make the peak sidelobe level (PSL) and stopband energy (SE) tradeoff explained in Adams and Sullivan (see IEEE Trans. on Signal Proc., vol. 46, p.306-20, 1998). Regular half-band filters designed in this way lead to regular orthogonal wavelets. This paper therefore presents a solution to all difficulties noted in Zarowski (see PACRIM'97, Victoria, BC, Canada, p.477-80, 1997).
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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".