A necessary and sufficient condition for the BIBO stability of general-order Bode-type variable-amplitude wave-digital equalizers
Bibliographic record
Abstract
Recently, the authors developed a new synthesis technique for the design of higher-order Bode-type variable-amplitude (VA) wave-digital (WD) equalizers. The salient feature of the resulting VA WD equalizers is that they permit the continuous variation of the WD equalizer transfer function from a shaping transfer function to its inverse by changing the value of a single variable digital multiplier only. The proposed design technique was based on the WD realization of the corresponding positive-real analog prototype shaping impedance function, and on the realization of the equalizer transfer function as the reflectance of the shaping impedance function with respect to the constituent variable digital multiplier. This paper is concerned with an investigation of the bounded-input bounded-output (BIBO) stability of general-order VA WD equalizers. It is shown that the resulting conditions are both necessary and sufficient for the BIBO stability of the VA WD equalizers for the entire range of values for the variable digital multiplier. These conditions can be checked in a straightforward fashion in terms of the characteristics of the shaping transfer function alone. An application example is given to illustrate 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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".