Structural interpretation of matched pole–zero discretisation
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Bibliographic record
Abstract
The paper deals with matched pole–zero discretisation, which has been used in practice for hand calculations in the digital redesign of continuous-time systems but available only in the transfer-function form. Since this form is inconvenient for characterising the time-domain properties of sampled-data loops and for computerising the design of such systems, a state–space formulation is developed. Under the new interpretation, the matched pole–zero model is shown to be structurally identical to a hold-equivalent discrete-time model, where the generalised hold takes integral part, thus unifying the most widely used discretisation approaches. An algorithm for obtaining the generalised hold function is presented. The hold-equivalent structure of the matched pole–zero model clarifies several discrete-time system properties, such as controllability and observability, and their preservation or loss with a matched pole–zero discretisation. With the proposed formulation, the matched pole–zero, hold-equivalent, and mapping models can now all be constructed with a single schematic model. This is of considerable practical importance in digital redesign, especially with the so-called plant-input mapping methods which use the matched pole–zero discretisation of the closed-loop system, and in digital simulations performed with a block-diagram language.
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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 | 0.000 |
| 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 it