Design of QMF banks and nonlinear optimization
Why this work is in the frame
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Bibliographic record
Abstract
This paper considers the design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters have linear phase and are of FIR. An iterative algorithm for minimizing the reconstruction error of QMF banks as well as the stopband error of the prototype filter has been developed in the literature. the authors' results provide new derivations for an explicit expression of the error function to be minimized and the necessary condition for minimality. These results offer new insight to the design of QMF banks and relates it to a more general nonlinear optimization problem. Moreover a new iterative algorithm is proposed that generalizes the one from Chen and Lee (1992). It is shown that this new algorithm is a descending one and is essentially a modified Newton's algorithm. Thus the iterative algorithm not only converges, but also admits a fast convergent rate.
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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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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