Generation of 1D and 2D analog and digital lowpass filters with monotonic amplitude-frequency response
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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 s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> domains. 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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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 | 0.002 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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