Minimax design of IIR digital filters using SDP relaxation technique
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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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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 | 0.000 |
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 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".