Stability and transient behavior of Bode-type variable-amplitude digital equalizers with dynamic variable multiplier variations
Bibliographic record
Abstract
In a previous publication, the theoretical basis provided by Kharitonov's stability theorem was exploited and applied to the development of a novel BIBO stability condition for general-order Bode-type variable-amplitude (VA) digital equalizers. This was achieved under the assumptions, (a) that the VA digital equalizer operates under infinite precision arithmetic, and (b) that it operates under "static" variable digital multiplier variations (i.e. variations which occur slowly or only after the transients resulting from the "dynamic" variations of the digital multiplier have died down to negligible levels). The present paper is concerned with an extension of the results to the investigation of the effect of "dynamic" variations of the variable digital multiplier on the stability and transient signal behaviour of the Bode-type VA digital equalizers both under infinite-precision as well as finite-precision digital equalizer operations. An analytical relationship is also derived for the estimation of the time required for the equalizer output signal transients to reduce to a specified negligible level. An application example is given to illustrate the practical application of the main results.
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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 | 0.001 | 0.004 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".