Structure‐induced low‐sensitivity design of sampled data and digital ladder filters using delta discrete‐time operator
Bibliographic record
Abstract
Abstract The concept of the delta discrete‐time operator‐based doubly terminated two‐pair (ladder) is discussed here for use in sampled‐data and digital filter design. The two‐pair filter utilizes traditional backward Euler and forward Euler integrators, is lossless under scaling (LUS), and possesses good magnitude sensitivity which is induced intrinsically due to the filter structure. This paper is an overview and consolidation of results published by the authors over the years in various conferences (Khoo et al., 1998, 1999, 2001, 2008, 2008a, 2008b) in a unifying and tutorial fashion. To achieve the low magnitude sensitivity, the well‐known Feldtkeller equation corresponding to the delta‐operator formulation is derived to establish the theoretical basis for the realization. One significant advantage of the design procedure presented here using the delta operator is that it overcomes the numerical problem at the spectral factorization stage of the conventional z‐domain lossless‐discrete‐time integrator (LDI) synthesis method when the filter poles are clustered around z = 1. Furthermore, the entire operation involves only rational polynomials, as opposed to fractional power polynomials as in the LDI and other methods in z‐domain. The method presented can realize three distinct forms of transfer functions with varied transmission zeros.
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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 | 0.000 | 0.001 |
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".