Minimal realization and L 2 -sensitivity analysis for 3-D separable-denominator digital filters
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Bibliographic record
Abstract
The problems of minimal state-space realization for a three-dimensional (3-D) separable-denominator digital filter and analysis of l 2 -sensitivity for the realized 3-D state-space model are investigated. First, a 3-D transfer function with separable denominator is expressed as a cascade connection of three one-dimensional (1-D) transfer functions by applying a minimal decomposition technique. Next, each 1-D transfer function is realized by a state-space model of minimal order. The l 2 -sensitivity of a 3-D separable-denominator transfer function with respect to the state-space paramters is then analyzed based on a pure l 2 norm. Finally, a numerical example is presented to evaluate the l 2 -sensitivity of a 3-D state-space model realized from a given 3-D separable-denominator digital filter.
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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 | 0.001 | 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