Finite-precision characterization of a class of Bode-type variable-amplitude digital bump equalizers
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Bibliographic record
Abstract
In a previous contribution, a set of realizability conditions was developed and applied to the design and enumeration of variable-amplitude digital bump equalizers. This paper is concerned with an investigation of the performance characteristics of these digital equalizers taking into account the non-ideal effects of finite-precision arithmetic. The necessary and sufficient conditions for the BIBO stability of these equalizers under infinite-precision arithmetic has been established in a recent paper. This paper, on the other hand, applies the results thus obtained to the development of a class of equalizers based on finite-precision characteristics and a technique for the selection of equalizers from this class based on the determination of the required internal signal wordlength to ensure guaranteed stable operation without overflow saturation and limit-cycles under finite-precision arithmetic.
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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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| 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