Minimax design of IIR digital filters using SDP relaxation technique
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Bibliographic record
Abstract
In this paper, a new iterative algorithm is proposed to design IIR digital filters in the minimax sense. Instead of directly minimizing the error limit of the approximation error, the proposed algorithm employs a bisection searching procedure to locate the minimum error limit. At each iteration, a feasibility problem with a given error limit is to be solved, which is constructed by applying the semidefinite programming (SDP) relaxation technique to transform the nonconvex approximation error into a convex form. In practice, however, the truly minimax solution cannot be always obtained by using this iterative procedure. Therefore, a regularization term needs to be incorporated in the objective of the feasibility problem at each iteration. Another bisection searching procedure is then deployed to find the minimum weight utilized in the regularized objective function of the feasibility problem. The stability of designed filters can be guaranteed by a monitoring strategy, which does not need to incorporate any other constraint to the formulation of the feasibility problem. The convergence of the proposed method can be guaranteed. The performances have been demonstrated by filter examples.
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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) | 0.000 | 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