Generation of 1D and 2D analog and digital lowpass filters with monotonic amplitude-frequency response
Bibliographic record
Abstract
In this work, we discuss a new design methodology to generate monotonic frequency-response filters. We start from Butterworth, Papoulis, Filanovsky and Bessel-Thomson filters. For each of these filters, all-possible lower-order filters having monotonic responses are segregated from the corresponding higher-order filters. These provide new sets of such filters. In addition, it is shown that higher order filters having monotonic responses can be obtained by appropriate combinations of the filters from these new sets. This permits one to generate a large number of low-pass 1D analog filters having monotonic responses. 2D filters having monotonic frequency responses are designed for the first time starting from the above proposed filters. The analog filters are obtained by suitably cascading the filters in s1and s2domains. Suitable 2D digital filters are obtained by employing the generalized bilinear transformations, the constants chosen to ensure stability and monotonicity. Suitable examples are provided
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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) | 0.003 | 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".