Design of nearly linear-phase recursive digital filters by using unconstrained least-pth minimax optimization
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Bibliographic record
Abstract
A method for the design of nearly linear-phase recursive digital filters is proposed. The recursive filter is assumed be a cascade arrangement of second-order biquadratic sections whose transfer functions are expressed in the polar form. An error function is formulated based on the difference between the actual complex frequency response of the filter and the desired frequency response. Then by using a least-pth minimax algorithm, the required design is obtained. The new method achieves filter stability through the use of a parameterization scheme based on the so-called sigmoid function and it incorporates a mechanism by which an arbitrary prescribed stability margin can be achieved. The optimization engine used in the least-pth algorithm is an unconstrained quasi-Newton algorithm based on the Broyden-Fletcher-Goldfarb-Shanno updating formula and it incorporates a nonuniform adaptive variable sampling technique to prevent spikes in the error function. Several filter design examples demonstrate that the proposed method is very efficient in terms of computational effort required since it is an unconstrained method and, furthermore, it can yield designs that are superior relative to some of the known state-of-the-art methods.
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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 | 0.003 |
| 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