Closed-form solutions for discrete-time elliptic transfer functions
Bibliographic record
Abstract
Presents closed-form solutions in explicit form for the direct derivation of discrete-time elliptic transfer functions having denormalized lowpass (LP), highpass (HP), bandpass (BP), or bandstop (BS) loss-frequency characteristics. The proposed method is based on the derivation of a suitable discrete-time z-domain normalized lowpass elliptic prototype reference transfer function and on the transformation of that transfer function into the desired discrete-time z-domain denormalized LP, HP, BP, or BS elliptic transfer function using a recently advanced z-to z frequency transformation technique. The required discrete-time z-domain normalized lowpass prototype reference transfer function is derived by establishing the fact that if it is related to a continuous-time s-domain normalized lowpass elliptic prototype reference transfer function through the conventional s-to-z bilinear frequency transformation. The parameters of the former as expressed in terms of Jacobian elliptic functions, are related to those of the latter through the ascending Landen transformation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".