Towards global design of orthogonal filter banks and wavelets
Why this work is in the frame
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Bibliographic record
Abstract
This paper investigates several design issues concerning two-channel conjugate quadrature (CQ) filter banks and orthogonal wavelets. It is well known that optimal designs of CQ filters and wavelets in least squares or minimax sense are nonconvex problems and to date only local solutions can be claimed. By virtue of recent progress in global polynomial optimization and direct design techniques for CQ filters, we in this paper present a design strategy that may be viewed as our endeavors towards global solutions for CQ filters. Two design scenarios are considered, namely the least squares designs with vanishing moment (VM) requirement, and equiripple (i.e. minimax) designs with VM requirement. Simulation studies are presented to verify our design concept for both LS and minimax designs of low-order CQ filters; and to evaluate and compare the proposed algorithms with existing design algorithms for high-order CQ filters.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it